Javascript Code Dump By Vatsal Patel
ID : 1 & Title : What Is Nerdamer?
//symbolic math expression evaluator written in javaScript // https://nerdamer.com/ // https://cdn.jsdelivr.net/npm/nerdamer@1.1.12/nerdamer.core.min.js
ID : 2 & Title : nerdamer.core.min.js dump
var nerdamer=function(e){"use strict";var d=new P,S=e.bigInt,k=e.bigDec;k.set({precision:250});var 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t.num=t.num.multiply(e.num),t.den=t.den.multiply(e.den),t.simplify()},divide:function(e){if(e.equals(0))throw new qe("Division by zero not allowed!");return this.clone().multiply(e.clone().invert()).simplify()},subtract:function(e){return this.clone().add(e.clone().neg())},neg:function(){return this.num=this.num.multiply(-1),this},add:function(e){var t=this.den,n=e.den,r=this.clone(),i=r.num,e=e.num;return t.equals(n)?r.num=i.add(e):(r.num=i.multiply(n).add(e.multiply(t)),r.den=t.multiply(n)),r.simplify()},mod:function(e){var t=this.clone(),e=e.clone();return t.num=t.num.multiply(e.den),t.den=t.den.multiply(e.den),e.num=e.num.multiply(this.den),e.den=e.den.multiply(this.den),t.num=t.num.mod(e.num),t.simplify()},simplify:function(){var e=S.gcd(this.num,this.den);return this.num=this.num.divide(e),this.den=this.den.divide(e),this},clone:function(){var e=new Fe;return e.num=new S(this.num),e.den=new S(this.den),e},decimal:function(e){var t=this.num.isNegative()?"-":"";if(this.num.equals(this.den))return"1";e=e||F.PRECISION,e++;for(var n=[],r=this.num.abs(),i=this.den,s=0;s<e;s++){var o=r.divide(i),a=r.subtract(o.multiply(i));if(n.push(o),a.equals(0))break;r=a.times(10)}var u=n.shift();if(0===n.length)return t+u.toString();if(s===e){for(var l=[],s=0;s<2;s++)l.unshift(n.pop());n.push(Math.round(l.join(".")))}return t+(u.toString()+"."+n.join(""))},toDecimal:function(e){return(e=e||F.PRECISION)?this.decimal(e):this.num/this.den},qcompare:function(e){return[this.num.multiply(e.den),e.num.multiply(this.den)]},equals:function(e){isNaN(e)||(e=new Fe(e));e=this.qcompare(e);return e[0].equals(e[1])},absEquals:function(e){isNaN(e)||(e=new Fe(e));e=this.qcompare(e);return e[0].abs().equals(e[1])},greaterThan:function(e){isNaN(e)||(e=new Fe(e));e=this.qcompare(e);return e[0].gt(e[1])},gte:function(e){return this.greaterThan(e)||this.equals(e)},lte:function(e){return this.lessThan(e)||this.equals(e)},lessThan:function(e){isNaN(e)||(e=new Fe(e));e=this.qcompare(e);return e[0].lt(e[1])},isInteger:function(){return this.den.equals(1)},negate:function(){return this.num=this.num.multiply(-1),this},invert:function(){var e,t=this.den;return this.num.equals(0)||(e=this.num.isNegative(),this.den=this.num.abs(),this.num=t,e&&(this.num=this.num.multiply(-1))),this},isOne:function(){return this.num.equals(1)&&this.den.equals(1)},sign:function(){return this.num.isNegative()?-1:1},abs:function(){return this.num=this.num.abs(),this},gcd:function(e){return Fe.quick(S.gcd(e.num,this.num),S.lcm(e.den,this.den))},toString:function(){return this.den.equals(1)?this.num.toString():this.num.toString()+"/"+this.den.toString()},valueOf:function(){return F.USE_BIG?new k(this.num.toString()).div(new k(this.den.toString())):this.num/this.den},isNegative:function(){return this.toDecimal()<0}},De.imaginary=function(){var e=new De(F.IMAGINARY);return e.imaginary=!0,e},De.infinity=function(e){var t=new De("Infinity");return-1===e&&t.negate(),t},De.shell=function(e,t){t=new De(t);return t.group=e,t.symbols={},t.length=0,t},De.unwrapSQRT=function(e,t){var n,r=e.power;return e.fname===z&&(e.isLinear()||t)&&((n=e.args[0].clone()).power=n.power.multiply(new Fe(.5)),n.multiplier=n.multiplier.multiply(e.multiplier),e=n,t&&(e.power=r.multiply(new Fe(.5)))),e},De.hyp=function(e,t){return e=e||new De(0),t=t||new De(0),d.sqrt(d.add(d.pow(e.clone(),new De(2)),d.pow(t.clone(),new De(2))))},De.toPolarFormArray=function(e){var t=e.realpart(),e=e.imagpart();return[De.hyp(t,e),t.equals(0)?d.parse("pi/2"):d.trig.atan(d.divide(e,t))]},De.unwrapPARENS=function(e){if(""!==e.fname)return e;var t=e.args[0];return t.power=t.power.multiply(e.power),t.multiplier=t.multiplier.multiply(e.multiplier),""===e.fname?De.unwrapPARENS(t):t},De.create=function(e,t){return d.parse("("+e+")^("+(t=void 0===t?1:t)+")")},De.prototype={getNth:function(e){var t=Se(d.pow(d.parse(this.multiplier),d.parse(e).invert())),n=d.parse(me(t));return Se(d.pow(n,d.parse(e))).equals(d.parse(this.multiplier))?n:t},isToNth:function(t){var n,e=this.getNth(t),e=ue(e);return this.group===Z?(n=!0,this.each(function(e){e.isToNth(t)||(n=!1)})):n=this.group===D||ue(d.divide(d.parse(this.power),d.parse(t))),e&&n},isSquare:function(){return this.isToNth(2)},isCube:function(){return this.isToNth(3)},isSimple:function(){return this.power.equals(1)&&this.multiplier.equals(1)},powSimp:function(){if(this.group!==Z)return this.clone();var t=[],e=this.multiplier.sign();this.each(function(e){e=e.power;if(ne(e)||e.equals(1))return this.clone();t.push(e)});var n,r=new Fe(c(t)),e=this.multiplier.sign(),i=this.multiplier.clone().abs(),s=Te.ifactor(i),o=new Fe(1),a=new Fe(1);for(n in s){var u=new Fe(s[n]);u.lessThan(r)||(u=u.divide(r).subtract(new Fe(1)),a=a.multiply(new Fe(n))),o=o.multiply(d.parse(E(n)+"^"+E(u)).multiplier)}var l=new De(a);this.each(function(e){(e=e.clone()).power=e.power.divide(r),l=d.multiply(l,e)});i=d.symfunction($,[l]);return i.power=r,i.multiplier=e<0?o.negate():o,i},equals:function(e){return ne(e)||(e=new De(e)),this.value===e.value&&this.power.equals(e.power)&&this.multiplier.equals(e.multiplier)&&this.group===e.group},abs:function(){var e=this.clone();return e.multiplier.abs(),e},gt:function(e){return ne(e)||(e=new De(e)),this.isConstant()&&e.isConstant()&&this.multiplier.greaterThan(e.multiplier)},gte:function(e){return ne(e)||(e=new De(e)),this.equals(e)||this.isConstant()&&e.isConstant()&&this.multiplier.greaterThan(e.multiplier)},lt:function(e){return ne(e)||(e=new De(e)),this.isConstant()&&e.isConstant()&&this.multiplier.lessThan(e.multiplier)},lte:function(e){return ne(e)||(e=new De(e)),this.equals(e)||this.isConstant()&&e.isConstant()&&this.multiplier.lessThan(e.multiplier)},isPoly:function(e){var t=this.group,n=this.power;if(!ue(n)||n<0)return!1;if(t===D||t===G||this.isConstant(!0))return!0;n=b(this);if(t===Z&&1===n.length){var r=n[0];if(!r)return!0;for(s in this.symbols){var i=this.symbols[s];if(i.group===H&&!i.args[0].isConstant())return!1;if(!i.contains(r)&&!i.isConstant(!0))return!1}return!0}if(this.isComposite()||t===Z&&e){if(!e&&1<n.length)return!1;for(var s in this.symbols)if(!this.symbols[s].isPoly(e))return!1;return!0}return!1},stripVar:function(t,e){var n;return this.group!==j&&this.group!==G||this.value!==t?this.group===Z&&this.isLinear()?(n=new De(1),this.each(function(e){e.contains(t,!0)||(n=d.multiply(n,e.clone()))}),n.multiplier=n.multiplier.multiply(this.multiplier)):this.group!==X||this.isLinear()?this.group===X&&this.isLinear()?(n=new De(0),this.each(function(e){e.contains(t)||((e=e.clone()).multiplier=e.multiplier.multiply(this.multiplier),n=d.add(n,e))}),n.equals(0)&&(n=new De(this.multiplier))):n=this.group===V&&this.power.contains(t,!0)||this.group===H&&this.contains(t)?new De(this.multiplier):this.clone():n=new De(this.multiplier):n=new De(e?0:this.multiplier),n},toArray:function(n,r){r=r||{arr:[],add:function(e,t){var n=this.arr[t];this.arr[t]=n?d.add(n,e):e}};var e=this.group;if(e===G&&this.contains(n))r.add(new De(this.multiplier),this.power);else if(e===Z){var t=this.stripVar(n),i=d.divide(this.clone(),t.clone()),i=i.isConstant()?0:i.power;r.add(t,i)}else if(e===j&&this.value===n)this.each(function(e,t){r.add(e.stripVar(n),t)});else if(e===X)this.each(function(e){e.toArray(n,r)});else{if(this.contains(n))throw new I("Cannot convert to array! Exiting");r.add(this.clone(),0)}r=r.arr;for(var s=0;s<r.length;s++)r[s]||(r[s]=new De(0));return r},hasFunc:function(e){var t=this.group===H||this.group===V;if(t&&!e||t&&this.contains(e))return!0;if(this.symbols)for(var n in this.symbols)if(this.symbols[n].hasFunc(e))return!0;return!1},sub:function(t,n){t=ne(t)?t.clone():d.parse(t),n=ne(n)?n.clone():d.parse(n),t.group!==D&&t.group!==B||K("Cannot substitute a number. Must be a variable");var r,e=!1,i=t.multiplier.equals(1),s=this.multiplier.clone();if(this.value===t.value&&(this.group!==j&&t.group!==j||this.group===j&&t.group===j))(i||t.multiplier.equals(this.multiplier))&&(t.isLinear()?r=n:t.power.equals(this.power)&&(r=n,e=!0),t.multiplier.equals(this.multiplier)&&(s=new Fe(1)));else if(this.group===Z||this.previousGroup===Z)r=new De(1),this.each(function(e){e=d.parse(e.sub(t,n));r=d.multiply(r,e)});else if(this.isComposite()){var o=this.clone();if(t.isComposite()&&o.isComposite()&&o.isLinear()&&t.isLinear()){var a,u=function(e,t){for(var n in e.symbols){n=e.symbols[n];if(n.isComposite()&&u(n,t)||n.equals(t))return!0}return!1};for(a in t.symbols)if(!u(o,t.symbols[a]))return o.clone();r=d.add(d.subtract(o.clone(),t),n)}else r=new De(0),o.each(function(e){r=d.add(r,e.sub(t,n))})}else if(this.group===V)r=d.parse(this.value).sub(t,n);else if(this.group===H){for(var l=[],c=0;c<this.args.length;c++){var p=this.args[c];ne(p)||(p=d.parse(p)),l.push(p.sub(t,n))}r=d.symfunction(this.fname,l)}return r?(e||(e=this.group===V?this.power.sub(t,n):d.parse(this.power),r=d.pow(r,e)),r.multiplier=r.multiplier.multiply(s),r):this.clone()},isMonomial:function(){if(this.group===G)return!0;if(this.group!==Z)return!1;for(var e in this.symbols)if(this.symbols[e].group!==G)return!1;return!0},isPi:function(){return this.group===G&&"pi"===this.value},sign:function(){return this.multiplier.sign()},isE:function(){return"e"===this.value},isSQRT:function(){return this.fname===z},isConstant:function(t,n){if(n&&this.group===Z)for(var e in this.symbols)if(this.symbols[e].isConstant(!0))return!0;if("functions"===t&&this.isComposite()){var r=!0;return this.each(function(e){e.isConstant(t,n)||(r=!1)},!0),r}if("all"===t&&(this.isPi()||this.isE()))return!0;if(t&&this.group===H){for(var i=0;i<this.args.length;i++)if(!this.args[i].isConstant(t))return!1;return!0}return t?oe(this):this.value===l},isImaginary:function(){if(this.imaginary)return!0;if(this.symbols)for(var e in this.symbols)if(this.symbols[e].isImaginary())return!0;return!1},realpart:function(){if(this.isConstant())return this.clone();if(this.imaginary)return new De(0);if(this.isComposite()){var t=new De(0);return this.each(function(e){t=d.add(t,e.realpart())}),t}return this.isImaginary()?new De(0):this.clone()},imagpart:function(){if(this.group===G&&this.isImaginary())return new De(this.multiplier);if(this.isComposite()){var t=new De(0);return this.each(function(e){t=d.add(t,e.imagpart())}),t}return this.group===Z?this.stripVar(F.IMAGINARY):new De(0)},isInteger:function(){return this.isConstant()&&this.multiplier.isInteger()},isLinear:function(e){if(e){if(this.isConstant())return!0;if(this.group===G)return this.value!==e||this.power.equals(1);if(this.isComposite()&&this.power.equals(1)){for(var t in this.symbols)if(!this.symbols[t].isLinear(e))return!1;return!0}return this.group===Z&&this.symbols[e]?this.symbols[e].isLinear(e):!1}return this.power.equals(1)},containsFunction:function(e){if("string"==typeof e&&(e=[e]),this.group===H&&-1!==e.indexOf(this.fname))return!0;if(this.symbols)for(var t in this.symbols)if(this.symbols[t].containsFunction(e))return!0;return!1},multiplyPower:function(e){if(this.group===D&&this.multiplier.equals(1))return this;var t,n=this.power;return this.group!==V&&e.group===D?(t=e.multiplier,this.group!==D||t.isInteger()||this.convert(B),this.power=n.equals(1)?t.clone():n.multiply(t),this.group===B&&ue(this.power)&&(this.value=Math.pow(this.value,this.power),this.toLinear(),this.convert(D))):(this.group!==V&&(n=new De(n),this.convert(V)),this.power=d.multiply(n,e)),this},setPower:function(e,t){return this.group===D&&this.multiplier.equals(1)||(this.group!==V||ne(e)?(n=!1,ne(e)&&(e.group===D?e=e.multiplier:n=!0),n=n?V:B,this.power=e,this.group===D&&n&&this.convert(n,t)):(this.group=this.previousGroup,delete this.previousGroup,this.group===D?(this.multiplier=new Fe(this.value),this.value=l):this.power=e)),this;var n},isInverse:function(){return this.group===V?this.power.multiplier.lessThan(0):this.power<0},clone:function(e){var t,n=e||new De(0),r=["value","group","length","previousGroup","imaginary","fname","args","isInfinity","scientific"],i=r.length;if(this.symbols)for(var s in n.symbols={},this.symbols)n.symbols[s]=this.symbols[s].clone();for(t=0;t<i;t++)void 0!==this[r[t]]&&(n[r[t]]=this[r[t]]);return n.power=this.power.clone(),n.multiplier=this.multiplier.clone(),this.isConversion&&(n.isConversion=this.isConversion),this.isUnit&&(n.isUnit=this.isUnit),n},toUnitMultiplier:function(e){return this.multiplier.num=new S(this.multiplier.num.isNegative()&&e?-1:1),this.multiplier.den=new S(1),this},toLinear:function(){return this.power.equals(1)||this.setPower(new Fe(1)),this},each:function(e,t){if(this.symbols)for(var n in this.symbols){var r=this.symbols[n];if(r.group===j&&t)for(var i in r.symbols)e.call(n,r.symbols[i],i);else e.call(this,r,n)}else e.call(this,this,this.value)},valueOf:function(){return this.group===D?this.multiplier.valueOf():0===this.power?1:0===this.multiplier?0:Pe(this,"decimals")},contains:function(e,t){e=String(e);var n=this.group;if(this.value===e)return!0;if(this.symbols)for(var r in this.symbols)if(this.symbols[r].contains(e,t))return!0;if(n===H||this.previousGroup===H)for(var i=0;i<this.args.length;i++)if(this.args[i].contains(e,t))return!0;if(n===V){if(t&&this.power.contains(e,t))return!0;if(this.value===e)return!0}return this.value===e},negate:function(){return this.multiplier.negate(),this.group!==X&&this.group!==j||this.distributeMultiplier(),this},invert:function(e,t){return e||(this.multiplier=this.multiplier.invert()),ne(this.power)?this.power.negate():this.group===Z&&t?this.each(function(e){return e.invert()}):this.power&&this.group!==D&&this.power.negate(),this},distributeMultiplier:function(e){e=e?this.power.absEquals(1):this.power.equals(1);if(this.symbols&&e&&this.group!==Z&&!this.multiplier.equals(1)){for(var t in this.symbols){t=this.symbols[t];t.multiplier=t.multiplier.multiply(this.multiplier),t.distributeMultiplier()}this.toUnitMultiplier()}return this},distributeExponent:function(){if(!this.power.equals(1)){var e,t=this.power;for(e in this.symbols){var n=this.symbols[e];n.group===V?n.power=d.multiply(n.power,new De(t)):this.symbols[e].power=this.symbols[e].power.multiply(t)}this.toLinear()}return this},convert:function(e,t){var n;return H<e?(n=this.clone(),this.symbols={},(e===Z?n:this).toUnitMultiplier(),this.group===H&&(n.args=this.args,delete this.args,delete this.fname),this.isImgSymbol&&delete 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n=e.realpart(),r=e.imagpart(),i=t.realpart(),s=t.imagpart(),e=H.multiply(n.clone(),i.clone()),t=H.multiply(r.clone(),s.clone()),r=H.multiply(i.clone(),r),n=H.multiply(n,s.clone()),s=H.add(H.pow(i,new Q(2)),H.pow(s,new Q(2)));return H.divide(H.add(H.add(e,t),H.multiply(H.subtract(r,n),Q.imaginary())),s)},trigSimp:function(e){var t,n,r,i,s,o;return e.containsFunction(["cos","sin","tan"])&&(e=e.clone(),n=(e=(t=_.Simplify.strip(e)).pop()).clone(),e.group===Z?(r=new Q(0),e.each(function(e){e=_.Simplify.trigSimp(e.fnTransform());r=H.add(r,e)},!0),n=H.pow(H.multiply(new Q(e.multiplier),r),new Q(e.power))):e.group===A&&(i=e.getNum(),s=e.getDenom(),(n="sin"===i.fname&&"cos"===s.fname&&i.args[0].equals(s.args[0])&&i.power.equals(s.power)?H.parse($.Utils.format("({0})*({1})*tan({2})^({3})",s.multiplier,i.multiplier,i.args[0],i.power)):n).group===A&&(o=new 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e.group===A&&(t=e.getDenom(),n=e.getNum().distributeMultiplier(),t=_.Simplify.fracSimp(t),n=_.Simplify.fracSimp(n),e=H.divide(n,t)),e},sqrtSimp:function(e,t){if(e.isSQRT()){var n,r,i=_.Factor.factor(e.args[0].clone()),s=H.parse(i.multiplier),o=s.sign(),a=H.sqrt(s.abs());if(I(a))return i.group===A?(n=new Q(1),i.each(function(e){var t;e.group===u?(t=H.sqrt(e.clone()),I(t)?a=H.multiply(a,t):n=H.multiply(n,e)):n=H.multiply(n,e)}),o=H.multiply(n,H.parse(o)),(r=H.sqrt(o.clone())).isImaginary&&(r=H.sqrt(H.expand(o.clone())))):r=H.sqrt(i.clone().toUnitMultiplier()),H.multiply(a,r)}else e.isComposite()&&e.isLinear()?(a=new Q(0),e.each(function(e){a=H.add(a,_.Simplify.sqrtSimp(e))},!0),a=H.multiply(a,H.parse(e.multiplier))):e.group===A&&(a=H.parse(e.multiplier),e.each(function(e){e=_.Simplify.sqrtSimp(e);a=H.multiply(a,e)},!0),a=H.pow(a,H.parse(e.power)));return a||H.parse(e)},patternSub:function(n){var r={},i=function(e){var t=!1;return e.each(function(e){e.group===Z?t=!0:e.symbols&&(t=i(e))}),t},s=function(e){e.each(function(e){var t;!e.symbols&&e.group!==x||(i(e)?s(e):r[e.value]||(t=$.Utils.getU(n),r[e.value]=t,n=n.sub(e.value,t)))},!0)};return s(n),[n,r]},simplify:function(e){var t=_.Simplify.strip(e);if(e=t.pop(),(e=_.Simplify.fracSimp(e)).isConstant()||e.group===$.groups.S)return t.push(e),_.Simplify.unstrip(t,e);var n,r=e.clone(),r=_.Simplify.trigSimp(r);return r=_.Simplify.ratSimp(r),(r=_.Factor.factor(r)).group===$.groups.CP&&r.isLinear()&&(e=r.multiplier.clone(),r.toUnitMultiplier(),n=new Q(0),r.each(function(e){e=_.Simplify.simplify(e);n=H.add(n,e)}),(r=n).multiplier=n.multiplier.multiply(e)),_.Simplify.unstrip(t,r)}},Classes:{Polynomial:W,Factors:U,MVTerm:J}};$.Expression.prototype.simplify=function(){return _.Simplify.simplify(this.symbol)},nerdamer.useAlgebraDiv=function(){var n=_.divideFn=H.divide,r=0;H.divide=function(e,t){t=1===++r?$.Algebra.divide(e,t):n(e,t);return 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_.line}},{name:"sqcomp",visible:!0,numargs:[1,2],build:function(){return function(t,e){try{return e=e||X(t)[0],_.sqComplete(t.clone(),e).f}catch(e){return t}}}}]),nerdamer.api()}(),"undefined"!=typeof module&&void 0===nerdamer&&(nerdamer=require("./nerdamer.core.js"),require("./Algebra.js")),function(){"use strict";var ct=nerdamer.getCore(),pt=ct.PARSER,ft=ct.Frac,ht=ct.Settings,mt=ct.Utils.isSymbol,gt=ct.groups.FN,dt=ct.Symbol,m=ct.Utils.text,vt=ct.Utils.inBrackets,wt=ct.Utils.isInt,yt=ct.Utils.format,bt=ct.Utils.even,k=ct.Utils.evaluate,g=ct.groups.N,St=ct.groups.S,gt=ct.groups.FN,Mt=ct.groups.PL,Nt=ct.groups.CP,Et=ct.groups.CB,qt=ct.groups.EX,d=ct.groups.P,xt=ht.LOG,At="sqrt",Ct="sin",Lt="cos",It="tan",Ut="sec",_t="csc",Rt="cot",Ot="asin",Tt="atan",Pt="sinh",kt="cosh",Ft="tanh";function Dt(e){this.message=e||""}Dt.prototype=new Error,dt.prototype.hasIntegral=function(){return this.containsFunction("integrate")},dt.prototype.fnTransform=function(){if(this.group!==gt)return this;var e,t,n,r=this.args[0],i=new dt(this.multiplier),s=this.clone().toUnitMultiplier();if(this.isLinear())switch(this.fname){case Pt:n=pt.parse(yt("(e^({0})-e^(-({0})))/2",r));break;case kt:n=pt.parse(yt("(e^({0})+e^(-({0})))/2",r));break;case Ft:n=pt.parse(yt("(e^({0})-e^(-({0})))/(e^({0})+e^(-({0})))",r));break;case It:n=pt.parse(yt("sin({0})/cos({0})",r));break;case _t:n=pt.parse(yt("1/sin({0})",r));break;case Ut:n=pt.parse(yt("1/cos({0})",r));break;default:n=s}else if(this.power.equals(2))switch(this.fname){case Ct:n=pt.parse(yt("1/2-cos(2*({0}))/2",r));break;case Lt:n=pt.parse(yt("1/2+cos(2*({0}))/2",r));break;case It:n=pt.parse(yt("sin({0})^2/cos({0})^2",r));break;case kt:n=pt.parse(yt("1/2+cosh(2*({0}))/2",r));break;case Pt:n=pt.parse(yt("-1/2+cosh(2*({0}))/2",r));break;case Ft:n=pt.parse(yt("(1+cosh(2*({0})))/(-1+cosh(2*({0})))",r));break;case Ut:n=pt.parse(yt("(1-cos(2*({0})))/(1+cos(2*({0})))+1",r));break;default:n=s}else this.fname===Ut?n=pt.parse(yt("1/cos({0})^({1})",this.args[0],this.power)):this.fname===_t?n=pt.parse(yt("1/sin({0})^({1})",this.args[0],this.power)):this.fname===It?n=this.power.lessThan(0)?pt.parse(yt("cos({0})^(-({1}))/sin({0})^({1})",this.args[0],this.power.negate())):pt.parse(yt("sin({0})^({1})/cos({0})^({1})",this.args[0],this.power)):this.fname===Ct&&this.power.lessThan(0)?n=pt.parse(yt("csc({0})^(-({1}))",this.args[0],this.power.negate())):this.fname===Lt&&this.power.lessThan(0)?n=pt.parse(yt("sec({0})^(-({1}))",this.args[0],this.power.negate())):this.fname===Ct&&this.power.equals(3)?n=pt.parse(yt("(3*sin({0})-sin(3*({0})))/4",this.args[0])):this.fname===Lt&&this.power.equals(3)?n=pt.parse(yt("(cos(3*({0}))+3*cos({0}))/4",this.args[0])):this.fname!==Lt&&this.fname!==Ct||!bt(this.power)?n=s:(t=this.power/2,e=pt.pow(this.clone().toLinear(),pt.parse(2)).fnTransform(),t=pt.expand(pt.pow(e,pt.parse(t))),n=new dt(0),t.each(function(e){e=e.fnTransform();n=pt.add(n,e)},!0));return pt.multiply(n,i)},dt.prototype.hasTrig=function(){if(this.isConstant(!0)||this.group===St)return!1;if(this.fname&&(ct.Utils.in_trig(this.fname)||ct.Utils.in_inverse_trig(this.fname)))return!0;if(this.symbols)for(var e in this.symbols)if(this.symbols[e].hasTrig())return!0;return!1},ct.Expression.prototype.hasIntegral=function(){return this.symbol.hasIntegral()},ct.Utils.toCommonDenominator=function(e){if(e.isComposite()&&e.isLinear()){var t=new dt(e.multiplier),n=new dt(1),r=new dt(0);return e.each(function(e){n=pt.multiply(n,e.getDenom())},!0),e.each(function(e){var t=e.getNum(),e=e.getDenom(),e=pt.multiply(t,pt.divide(n.clone(),e));r=pt.add(r,e)}),pt.multiply(t,ct.Algebra.divide(pt.expand(r),pt.expand(n)))}return e},ct.Utils.in_inverse_trig=function(e){return-1!==[Ot,"acos",Tt,"acsc","asec","acot"].indexOf(e)},ct.Utils.in_trig=function(e){return-1!==[Lt,Ct,It,Ut,_t,Rt].indexOf(e)},ct.Utils.in_htrig=function(e){return-1!==[Pt,kt,Ft,"acsch","asech","acoth"].indexOf(e)},ct.Matrix.jacobian=function(e,t){var i=new ct.Matrix;return(t=t||ct.Utils.arrayGetVariables(e)).forEach(function(n,r){e.forEach(function(e,t){e=ct.Calculus.diff(e.clone(),n);i.set(t,r,e)})}),i},ct.Matrix.prototype.max=function(){var t=new dt(0);return this.each(function(e){e=e.abs();e.gt(t)&&(t=e)}),t},ct.Matrix.cMatrix=function(n,e){var r=new ct.Matrix;return e.forEach(function(e,t){r.set(t,0,pt.parse(n))}),r};var Bt=ct.Utils.all_functions=function(e){for(var t=0,n=e.length;t<n;t++)if(e[t].group!==gt)return!1;return!0},l=ct.Utils.cosAsinBtranform=function(e,t){e=e.args[0],t=t.args[0];return pt.parse(yt("(sin(({0})+({1}))-sin(({0})-({1})))/2",e,t))},c=ct.Utils.cosAsinAtranform=function(e,t){if(1!==Number(t.power))return pt.multiply(e,t);e=e.args[0];return pt.parse(yt("(sin(2*({0})))/2",e))},p=ct.Utils.cosAsinBtranform=function(e,t){e=e.args[0],t=t.args[0];return pt.parse(yt("(cos(({0})+({1}))-cos(({0})-({1})))/2",e,t))},Gt=ct.Utils.trigTransform=function(e){for(var t,n,r,i,s={},o=new dt(1),a=0,u=e.length;a<u;a++)(r=e[a]).group===gt?(n=r.fname)===Lt&&s.sin?(t=(s.sin.args[0].toString()!==r.args[0].toString()?l:c)(r,s.sin),delete s.sin,o=pt.multiply(o,t)):n===Ct&&s.cos?(t=(s.cos.args[0].toString()!==r.args[0].toString()?l:c)(r,s.cos),delete s.cos,o=pt.multiply(o,t)):n===Ct&&s.sin?(t=s.sin.args[0].toString()!==r.args[0].toString()?p(r,s.sin):pt.multiply(r,s.sin),delete s.sin,o=t):s[n]=r:o=pt.multiply(o,r);for(i in s)o=pt.multiply(o,s[i]);return o};ct.Settings.integration_depth=10,ct.Settings.max_lim_depth=10;var Vt=ct.Calculus={version:"1.4.6",sum:function(s,o,a,u){if(o.group!==ct.groups.S)throw new ct.exceptions.NerdamerTypeError("Index must be symbol. "+m(o)+" provided");var e;return o=o.value,ct.Utils.isNumericSymbol(a)&&ct.Utils.isNumericSymbol(u)?(e=u-a<200?"":"PARSE2NUMBER",a=Number(a),u=Number(u),ct.Utils.block(e,function(){for(var e=s.text(),t={"~":!0},n=new ct.Symbol(0),r=a;r<=u;r++){t[o]=new dt(r);var i=pt.parse(e,t),n=pt.add(n,i)}return n})):pt.symfunction("sum",arguments)},product:function(i,s,o,a){if(s.group!==ct.groups.S)throw new ct.exceptions.NerdamerTypeError("Index must be symbol. "+m(s)+" provided");return s=s.value,ct.Utils.isNumericSymbol(o)&&ct.Utils.isNumericSymbol(a)?ct.Utils.block(a-o<200?"":"PARSE2NUMBER",function(){o=Number(o),a=Number(a.multiplier);for(var e=i.text(),t={},n=new ct.Symbol(1),r=o;r<=a;r++)t[s]=new dt(r),n=pt.multiply(n,pt.parse(e,t));return n}):pt.symfunction("product",arguments)},diff:function(e,l,r){if(ct.Utils.isVector(e)){var t=new ct.Vector([]);return e.each(function(e){t.elements.push(Vt.diff(e,l,r))}),t}if(ct.Utils.isMatrix(e)){var i=new ct.Matrix;return e.each(function(e,t,n){i.set(t,n,Vt.diff(e,l,r))}),i}var n,s,c=mt(l)?l.text():l;return r=mt(r)?r.multiplier:r||1,void 0===c&&(c=ct.Utils.variables(e)[0]),e.group===gt&&e.fname===At&&(s=e.args[0],n=e.power.clone(),s.group===g&&s.group===d||(s.power=mt(s.power)?pt.multiply(s.power,pt.multiply(new dt(.5)),n):s.power.multiply(new ft(.5)).multiply(n),s.multiplier=s.multiplier.multiply(e.multiplier)),e=s),e=e.group!==gt||mt(e.power)?f(e):(n=f(pt.parse(e)),s=Vt.diff(e.args[0].clone(),c),pt.multiply(n,s)),e=1<r?Vt.diff(e,l,--r):e;function p(e){return e.value!==c&&!e.contains(c,!0)||(e.multiplier=e.multiplier.multiply(e.power),e.power=e.power.subtract(new ft(1)),e.power.equals(0)&&(e=dt(e.multiplier))),e}function f(e){var t=e.group;if(t===g||t===St&&e.value!==c||t===d)e=dt(0);else if(t===St)e=p(e);else{if(t===Et){var n=e.multiplier.clone();e.toUnitMultiplier();var r=pt.multiply(function(e){for(var t=e.collectSymbols(),n=new dt(0),r=t.length,i=0;i<r;i++){for(var s=Vt.diff(t[i].clone(),c),o=0;o<r;o++)i!==o&&(s=pt.multiply(s,t[o].clone()));n=pt.add(n,s)}return n}(e),p(e));return r.multiplier=r.multiplier.multiply(n),r}if(t===gt&&e.power.equals(1))switch(e.fname){case xt:s=e.clone(),(e=e.args[0].clone()).power=e.power.negate(),e.multiplier=s.multiplier.divide(e.multiplier);break;case Lt:e.fname=Ct,e.multiplier.negate();break;case Ct:e.fname=Lt;break;case It:e.fname=Ut,e.power=new ft(2);break;case Ut:e=h(e,It);break;case _t:e=h(e,"-cot");break;case Rt:e.fname=_t,e.multiplier.negate(),e.power=new ft(2);break;case Ot:e=pt.parse("(sqrt(1-("+m(e.args[0])+")^2))^(-1)");break;case"acos":e=pt.parse("-(sqrt(1-("+m(e.args[0])+")^2))^(-1)");break;case Tt:e=pt.parse("(1+("+m(e.args[0])+")^2)^(-1)");break;case"abs":n=e.multiplier.clone(),e.toUnitMultiplier(),(o=e.args[0].clone()).toUnitMultiplier(),(e=pt.parse(vt(m(e.args[0]))+"/abs"+vt(m(o)))).multiplier=n;break;case"parens":e=dt(1);break;case"cosh":e.fname="sinh";break;case"sinh":e.fname="cosh";break;case Ft:e.fname="sech",e.power=new ft(2);break;case"sech":e=h(e,"-tanh");break;case"csch":var i=String(e.args[0]);return pt.parse("-coth("+i+")*csch("+i+")");case"coth":i=String(e.args[0]);return pt.parse("-csch("+i+")^2");case"asinh":e=pt.parse("(sqrt(1+("+m(e.args[0])+")^2))^(-1)");break;case"acosh":e=pt.parse("(sqrt(-1+("+m(e.args[0])+")^2))^(-1)");break;case"atanh":e=pt.parse("(1-("+m(e.args[0])+")^2)^(-1)");break;case"asech":i=String(e.args[0]);e=pt.parse("-1/(sqrt(1/("+i+")^2-1)*("+i+")^2)");break;case"acoth":e=pt.parse("-1/(("+e.args[0]+")^2-1)");break;case"acsch":i=String(e.args[0]);e=pt.parse("-1/(sqrt(1/("+i+")^2+1)*("+i+")^2)");break;case"asec":i=String(e.args[0]);e=pt.parse("1/(sqrt(1-1/("+i+")^2)*("+i+")^2)");break;case"acsc":i=String(e.args[0]);e=pt.parse("-1/(sqrt(1-1/("+i+")^2)*("+i+")^2)");break;case"acot":e=pt.parse("-1/(("+e.args[0]+")^2+1)");break;case"S":i=String(e.args[0]);e=pt.parse("sin((pi*("+i+")^2)/2)");break;case"C":i=String(e.args[0]);e=pt.parse("cos((pi*("+i+")^2)/2)");break;case"Si":i=e.args[0];e=pt.parse("sin("+i+")/("+i+")");break;case"Shi":i=e.args[0];e=pt.parse("sinh("+i+")/("+i+")");break;case"Ci":i=e.args[0];e=pt.parse("cos("+i+")/("+i+")");break;case"Chi":i=e.args[0];e=pt.parse("cosh("+i+")/("+i+")");break;case"Ei":i=e.args[0];e=pt.parse("e^("+i+")/("+i+")");break;case"Li":i=e.args[0];e=pt.parse("1/"+ht.LOG+"("+i+")");break;case"erf":e=pt.parse("(2*e^(-("+e.args[0]+")^2))/sqrt(pi)");break;case"atan2":var s=String(e.args[0]),i=String(e.args[1]);e=pt.parse("("+i+")/(("+i+")^2+("+s+")^2)");break;case"sign":e=new dt(0);break;case"sinc":e=pt.parse(yt("(({0})*cos({0})-sin({0}))*({0})^(-2)",e.args[0]));break;case ht.LOG10:e=pt.parse("1/(("+e.args[0]+")*"+ht.LOG+"(10))");break;default:e=pt.symfunction("diff",[e,l])}else if(t===qt||t===gt&&mt(e.power)){var r=t===qt?e.value:t===gt&&e.contains(c)?e.fname+vt(m(e.args[0])):e.value+vt(m(e.args[0])),o=(pt.multiply(pt.parse(xt+vt(r)),e.power.clone()),Vt.diff(pt.multiply(pt.parse(xt+vt(r)),e.power.clone()),c));e=pt.multiply(e,o)}else if(t!==gt||e.power.equals(1)){if(t===Nt||t===Mt){var a,t=e.clone(),u=new dt(0);for(a in e.symbols)u=pt.add(u,Vt.diff(e.symbols[a].clone(),c));e=pt.multiply(p(t),u)}}else(o=e.clone()).toLinear(),o.toUnitMultiplier(),e=pt.multiply(p(e.clone()),f(o))}return e.updateHash(),e}function h(e,t,n){return pt.multiply(e,pt.parse(t+vt(n||m(e.args[0]))))}},integration:{u_substitution:function(e,i){function t(e,t,n){var r=Vt.diff(t,i),r=n?n(e,t):pt.divide(e.clone(),r);return r.contains(i,!0)?null:r}function n(e,t){e=Vt.integrate(pt.symfunction(e,[new dt(u)]),u,0);return(e=e.sub(new dt(u),t)).updateHash(),e}var r,s=e[0].clone(),o=e[1].clone(),a=s.group,e=o.group,u="__u__";if(a===gt&&e!==gt)return(r=t(o,(c=s.args[0]).clone()))?pt.multiply(r,n(s.fname,c)):(r=t(o,s))?Vt.integration.poly_integrate(s):void 0;if(e===gt&&a!==gt){if(r=t(s,(c=o.args[0]).clone()))return pt.multiply(r,n(o.fname,c))}else{if(a===gt&&e===gt)return(r=t(s.clone(),o.clone()))||(r=t(o.clone(),s.clone()))?pt.multiply(Vt.integration.poly_integrate(o),r):void 0;if(a===qt&&e!==qt){if(!(r=t(o,(p=s.power).clone()))){var l=Vt.integration.decompose_arg(p.clone(),i),c=Vt.diff(l[2].clone(),i),c=Vt.integration.decompose_arg(c.clone(),i);if(pt.multiply(l[1],c[1]).power.equals(o.power)){c=pt.divide(l[0].clone(),c[0].clone()),c=pt.multiply(c.clone(),pt.pow(new dt(s.value),pt.multiply(l[0],new dt(u)))),c=pt.multiply(c,new dt(u));return Vt.integration.by_parts(c,u,0,{}).sub(u,l[1].clone())}}l=Vt.integrate(s.sub(p.clone(),new dt(u)),u,0);return pt.multiply(l.sub(new dt(u),p),r)}if(e===qt&&a!==qt){r=t(s,(p=o.power).clone());l=Vt.integrate(o.sub(p,new dt(u)),u,0);return pt.multiply(l.sub(new dt(u),p),r)}if(s.isComposite()||o.isComposite()){var a=function(e,t){t=Vt.diff(t,i),e=ct.Algebra.Factor.factor(e),t=ct.Algebra.Factor.factor(t);return pt.divide(e,t)},l=s.isComposite()?s.clone().toLinear():s.clone(),p=o.isComposite()?o.clone().toLinear():o.clone();return(r=t(l.clone(),p.clone(),a))?pt.multiply(Vt.integration.poly_integrate(o),r):(r=t(p.clone(),l.clone(),a))?pt.multiply(Vt.integration.poly_integrate(s),r):void 0}}},poly_integrate:function(e){var t=e.power.toString(),n=e.multiplier.toDecimal(),e=e.toUnitMultiplier().toLinear();return-1===Number(t)?pt.multiply(new dt(n),pt.symfunction(xt,[e])):pt.parse(yt("({0})*({1})^(({2})+1)/(({2})+1)",n,e,t))},stop:function(e){throw ct.Utils.warn(e=e||"Unable to compute integral!"),new Dt(e)},partial_fraction:function(e,t,n,r){var i;return mt(t)||(t=pt.parse(t)),i=new dt(0),(e=ct.Algebra.PartFrac.partfrac(e,t)).group===Et&&e.isLinear()?(e.each(function(e){e.isLinear()||Vt.integration.stop()}),e.each(function(e){i=pt.add(i,Vt.integrate(e,t,n,r))})):i=pt.add(i,Vt.integrate(e,t,n,r)),i},get_udv:function(e){function t(e){var t,n=e.group;n===gt?(t=e.fname,ct.Utils.in_trig(t)||ct.Utils.in_htrig(t)?r[3].push(e):ct.Utils.in_inverse_trig(t)?r[1].push(e):t===xt?r[0].push(e):Vt.integration.stop()):n===St||e.isComposite()&&e.isLinear()||n===Et&&e.isLinear()?r[2].push(e):n===qt||e.isComposite()&&!e.isLinear()?r[4].push(e):Vt.integration.stop()}var r=[[],[],[],[],[]];e.group===Et?e.each(function(e){t(dt.unwrapSQRT(e,!0))}):t(e);for(var n,i=new dt(1),s=0;s<5;s++){var o=r[s],a=o.length;if(0<a){if(1<a)for(var u=new dt(1),l=0;l<a;l++)u=pt.multiply(u,o[l].clone());else u=o[0].clone();n?i=pt.multiply(i,u):(n=u).multiplier=n.multiplier.multiply(e.multiplier)}}return[n,i]},trig_sub:function(e,t,n,r,i,s){(i=i||Vt.integration.decompose_arg(e.clone().toLinear(),t))[3],i[2];var o=i[0],a=i[1];if(a.power.equals(2)&&o.greaterThan(0)){t=ct.Utils.getU(e),i=pt.parse(It+vt(t)),o=pt.parse(Ut+vt(t)+"^2"),o=pt.multiply(e.sub(a,i),o),a=Vt.integrate(o,t,n,r).sub(i,a);return ct.Utils.clearU(i),a}},by_parts:function(e,t,n,r){var i,s,o,a,u,l;return r.previous=r.previous||[],o=(s=Vt.integration.get_udv(e))[0],i=s[1],u=(a=dt.unwrapSQRT(pt.expand(Vt.diff(o.clone(),t)),!0)).clone().stripVar(t),a=pt.divide(a,u.clone()),e=Vt.integrate(i.clone(),t,n||0),a=(s=pt.multiply(e.clone(),a)).toString(),-1!==r.previous.indexOf(a)&&ct.Utils.in_trig(o.fname)&&i.isE()?(r.is_cyclic=!0,new dt(1)):(r.previous.push(a),o=pt.multiply(o,e),e=s.multiplier.clone(),s.toUnitMultiplier(),(u=pt.multiply(Vt.integrate(s.clone(),t,n,r),u)).multiplier=u.multiplier.multiply(e),u=pt.subtract(o,u),r.is_cyclic&&(r.previous.pop(),0===r.previous.length&&(u=pt.expand(u),l=new dt(0),u.each(function(e){e.contains(t)||(l=pt.add(l,e.clone()))}),u=pt.divide(pt.subtract(u,l.clone()),pt.subtract(new dt(1),l)))),u)},decompose_arg:ct.Utils.decompose_fn},integrate:function(ot,at,ut,lt){var e;if(at||(e=ct.Utils.variables(ot),at=(at=1===e.length?e[0]:at)||"x"),ct.Utils.isVector(ot)){var t=new ct.Vector([]);return ot.each(function(e){t.elements.push(Vt.integrate(e,at))}),t}return isNaN(at)||pt.error("variable expected but received "+at),ot.isConstant(!0)?pt.multiply(ot.clone(),pt.parse(at)):(lt=lt||{},ct.Utils.block("PARSE2NUMBER",function(){ut=ut||0;var t,n=mt(at)?at.toString():at,e=(ce=dt.unwrapSQRT(ot.clone(),!0)).group;try{if(++ut>ct.Settings.integration_depth&&Vt.integration.stop("Maximum depth reached. Exiting!"),ce.contains(n,!0)){if(e===St)t=Vt.integration.poly_integrate(ce,n,ut);else if(e===qt)if(ce.previousGroup===gt&&"sqrt"!==ce.fname&&ce.fname!==ht.PARENTHESIS&&Vt.integration.stop(),ce.contains(n)&&ce.previousGroup!==gt)ce.power.contains(n)?Vt.integration.stop():((We=Vt.diff(ce.clone().toLinear(),n)).contains(n)&&Vt.integration.stop(),t=Vt.integration.poly_integrate(ce,n,ut));else{if((f=Vt.diff(ce.power.clone(),n)).contains(n)){var r=f.stripVar(n);if((h=pt.divide(f.clone(),r.clone())).group===St&&h.isLinear())return r.multiplier=r.multiplier.divide(new ft(2)),pt.parse(yt("({2})*(sqrt(pi)*erf(sqrt(-{0})*{1}))/(2*sqrt(-{0}))",r,n,ce.multiplier));Vt.integration.stop()}ce.isE()?f.isLinear()?t=ce:f.isE()&&f.power.group===St&&f.power.power.equals(1)?t=pt.multiply(pt.symfunction("Ei",[ce.power.clone()]),ce.power):Vt.integration.stop():(g=pt.symfunction(xt,[pt.parse(ce.value)]),t=pt.divide(ce,g)),t=pt.divide(t,f)}else if(ce.isComposite()&&ce.isLinear()){var i=pt.parse(ce.multiplier);ce.toUnitMultiplier(),t=new dt(0),ce.each(function(e){t=pt.add(t,Vt.integrate(e,n,ut))}),t=pt.multiply(i,t)}else if(e===Nt)if((ce=ce.power.greaterThan(1)?pt.expand(ce):ce).power.equals(1))t=new dt(0),ce.each(function(e){t=pt.add(t,Vt.integrate(e,n,ut))},!0);else{var s=Number(ce.power),i=ce.multiplier.clone();ce.toUnitMultiplier();var o,a,u,l=ce.clone().toLinear(),c=(Ve=Vt.integration.decompose_arg(l,n))[3],p=Ve[2],f=Ve[0],h=Ve[1];if(-1===s&&h.group!==Mt&&h.power.equals(2)){var m,g,d,v,w,y,b,S,M,N,E,q=!wt(c)||0<c;t=h.group===St&&h.power.equals(2)&&q?(m=function(e){var t=new dt(1);return e.each(function(e){t=pt.multiply(t,"abs"===e.fname?e.args[0]:e)}),t},d=f.clone(),v=c.clone(),d=pt.pow(d,new dt(.5)),v=pt.pow(v,new dt(.5)),g=pt.multiply(m(v),m(d)),O=pt.symfunction(Tt,[pt.divide(pt.multiply(f,h.toLinear()),g.clone())]),pt.divide(O,g)):h.group===St&&h.isLinear()?pt.divide(Vt.integration.poly_integrate(ce),f):h.power.equals(4)?(E=vt,d=pt.parse(At+E(f)+"*"+n+"^2"),v=pt.parse(At+E(2)+"*"+E(f)+"^"+E("1/4")+"*"+E(c)+"^"+E("1/4")+"*"+n),w=pt.parse(At+E(c)),P=pt.add(pt.add(d.clone(),v.clone()),w.clone()),Z=pt.add(pt.subtract(d,v),w),y=pt.parse(At+E(2)+"*"+E(c)+"^"+E("3/4")),b=pt.parse(At+E(c)+"*"+E(c)+"^"+E("1/4")+"*"+n),S=pt.parse("2*"+E(c)+"*"+At+E(2)+"*"+E(c)+"^"+E("1/4")),M=pt.divide(pt.subtract(y.clone(),b.clone()),pt.multiply(S.clone(),Z)),N=pt.divide(pt.add(y,b),pt.multiply(S,P.clone())),pt.add(Vt.integrate(M,n,ut,lt),Vt.integrate(N,n,ut,lt))):Vt.integration.partial_fraction(ce,n,ut)}else if(-.5===s)h.group===St&&h.power.equals(2)&&p.multiplier.lessThan(0)&&!c.multiplier.lessThan(0)?(f.negate(),t=c.isConstant()&&f.isConstant()?(g=pt.symfunction(At,[f.clone()]),o=pt.symfunction(At,[pt.multiply(f.clone(),c)]),pt.divide(pt.symfunction(Ot,[pt.divide(p.toLinear(),o)]),g)):(a=pt.symfunction(At,[f]),u=pt.multiply(a.clone(),h.clone().toLinear()),pt.divide(pt.symfunction(Tt,[pt.divide(u,pt.symfunction(At,[l.clone()]))]),a))):Vt.integration.stop();else if(h.isLinear()&&h.group!==Mt)t=pt.divide(Vt.integration.poly_integrate(ce),f);else{if(h.power.equals(2)&&f.greaterThan(0)){var x=pt.parse(At+vt(f)),A=pt.parse(At+vt(c)),C=pt.multiply(x.clone(),A.clone()).invert(),L=pt.pow(c,new dt(ce.power)),I=ct.Utils.getU(ce);$e=pt.multiply(C,h.clone().toLinear());var U=pt.parse(Tt+vt($e)),_=2*(Math.abs(ce.power)-1),R=Vt.integrate(pt.parse(Lt+vt(I)+"^"+_));return ct.Utils.clearU(I),pt.multiply(R.sub(I,U),L)}if(ce.group===Et||ce.power.lessThan(0)){var O=ce.clone().toLinear(),T=ct.Algebra.Factor.factor(O).toString()!==O.toString();if(ct.Algebra.degree(O,pt.parse(n)).equals(2)&&!T)try{var P,k,F=ct.Algebra.sqComplete(O,n);$e=ct.Utils.getU(O),P=F.f.sub(F.a,$e),k=pt.pow(P,pt.parse(ce.power)),t=Vt.integrate(k,$e).sub($e,F.a)}catch(e){Vt.integration.stop()}else t=Vt.integration.partial_fraction(ce,n,ut,lt)}else t=Vt.integration.by_parts(ce,n,ut,lt)}t.multiplier=t.multiplier.multiply(i)}else if(e===gt){var D=ce.args[0],i=ce.multiplier.clone();ce.toUnitMultiplier();var B,G,V,H,j,Z,X,$,z,f=(Ve=Vt.integration.decompose_arg(D,n))[0],h=Ve[1],Q=ce.fname;if(Q===xt||Q===Ot||"acos"===Q||Q===Tt&&h.isLinear()){var Y,s=ce.power.toString();wt(s)&&(ut-=s),t=D.isComposite()?($e=ct.Utils.getU(ce),O=pt.pow(pt.parse(xt+vt($e)),new dt(s)),Ce=Vt.diff(D,n),Y=pt.multiply(O,Ce),R=Vt.integrate(Y,$e,ut,lt),pt.multiply(pt.parse(i),R.sub($e,D))):pt.multiply(pt.parse(i),Vt.integration.by_parts(ce,n,ut,lt))}else{if(Q===It&&ce.power.lessThan(0))return(Je=ce.clone()).power.negate(),Je.fname=Rt,pt.multiply(pt.parse(i),Vt.integrate(Je,n,ut));if(!f.contains(n,!0)&&ce.isLinear())if("abs"===Q)(h=pt.divide(D.clone(),f.clone())).group!==St||h.power.lessThan(0)?Vt.integration.stop():t=ct.Utils.even(h.power)?Vt.integrate(D,n,ut):((z=Vt.integrate(h,n,ut)).power=z.power.subtract(new ft(1)),pt.multiply(pt.multiply(pt.symfunction("abs",[h.toLinear()]),z),f));else{var W=ce.args[0].group,J=Vt.integration.decompose_arg(D,n);switch((W!==Nt&&W!==St&&W!==Et||!J[1].power.equals(1)||D.hasFunc())&&Vt.integration.stop(),Q){case Lt:t=pt.symfunction(Ct,[D]);break;case Ct:(t=pt.symfunction(Lt,[D])).negate();break;case It:t=pt.parse(yt(ht.LOG+"(sec({0}))",D));break;case Ut:t=pt.parse(yt(ht.LOG+"(tan({0})+sec({0}))",D));break;case _t:t=pt.parse(yt("-"+ht.LOG+"(csc({0})+cot({0}))",D));break;case Rt:t=pt.parse(yt(ht.LOG+"(sin({0}))",D));break;case Pt:t=pt.symfunction(kt,[D]);break;case kt:t=pt.symfunction(Pt,[D]);break;case Ft:t=pt.parse(yt(ht.LOG+"(cosh({0}))",D));break;case"asec":case"acsc":case"acot":case"asech":case"acsch":case"acoth":t=Vt.integration.by_parts(ce,n,ut,lt);break;case"sech":t=pt.parse(yt("atan(sinh({0}))",D));break;case"csch":t=pt.parse(yt(ht.LOG+"(tanh(({0})/2))",D));break;case"coth":t=pt.parse(yt(ht.LOG+"(sinh({0}))",D));break;case"exp":t=Vt.integrate(pt.parse(yt("e^({0})",D)),n,ut);break;case"S":var D=ce.args[0].clone(),K=(Se=Vt.integration.decompose_arg(D,n))[1],ee=Se[0],te=Se[3];t=pt.parse(yt("(cos((1/2)*pi*(({1})+({0})*({2}))^2)+pi*(({1})+({0})*({2}))*S(({1})+({0})*({2})))/(({0})*pi)",ee,te,h));break;case"C":D=ce.args[0].clone(),K=(Se=Vt.integration.decompose_arg(D,n))[1],ee=Se[0],te=Se[3];t=pt.parse(yt("(pi*(({1})+({0})*({2}))*C(({1})+({0})*({2}))-sin((1/2)*pi*(({1})+({0})*({2}))^2))/(({0})*pi)",ee,te,K));break;case"erf":D=ce.args[0].clone(),K=(Se=Vt.integration.decompose_arg(D,n))[1],ee=Se[0];t=pt.parse(yt("e^(-(({2}))^2)/(({0})*sqrt(pi))+(1/({0})+({1}))*erf(({2}))",ee,K,D));break;case"sign":t=pt.multiply(ce.clone(),D.clone());break;default:Vt.integration.stop()}t=pt.divide(t,f)}else h.isLinear()?Q===Lt||Q===Ct?(s=Number(ce.power),t=s<0?(ce.fname=Q===Ct?_t:Ut,ce.invert().updateHash(),Vt.integrate(ce,n,ut)):(D=ce.args[0],B=ce.clone(),G=ce.clone(),Ie=new dt((s-1)/s),V=pt.multiply(f.clone(),new dt(s)).invert(),B.power=B.power.subtract(new ft(1)),G.power=G.power.subtract(new ft(2)),We=pt.symfunction(Q===Lt?Ct:Lt,[D.clone()]),Q===Ct&&We.negate(),pt.add(pt.multiply(pt.multiply(V,B),We),pt.multiply(Ie,Vt.integrate(pt.parse(G),n,ut))))):Q===It||Q===Rt?ce.args[0].isLinear(n)&&(_=ce.power.subtract(new ft(1)).toString(),nt=ce.clone().toUnitMultiplier(),$=pt.parse(yt((Q===Rt?"-":"")+"1/({2}*{0})*{3}({1})^({0})",_,D,f,Q)),nt.power=nt.power.subtract(new ft(2)),nt.power.equals(0)&&(nt=pt.parse(nt)),t=pt.subtract($,Vt.integrate(nt,n,ut))):Q===Ut||Q===_t?(H=ce.power.subtract(new ft(1)).toString(),j=ce.power.subtract(new ft(2)).toString(),Z=Q===Ut?It:Rt,nt=ce.clone().toUnitMultiplier(),X=yt((Q===_t?"-":"")+"1/({0}*{1})*{4}({3})^({2})*{5}({3})",f,H,j,D,Q,Z),$=pt.parse(X),nt.power=nt.power.subtract(new ft(2)),nt.power.equals(0)&&(nt=pt.parse(nt)),t=pt.add($,pt.multiply(new dt(j/H),Vt.integrate(nt,n,ut)))):Q!==kt&&Q!==Pt||!ce.power.equals(2)?Vt.integration.stop():t=Vt.integrate(ce.fnTransform(),n,ut):Vt.integration.stop();t.multiplier=t.multiplier.multiply(i)}}else if(e===Mt)t=Vt.integration.partial_fraction(ce,n,ut);else if(e===Et){var ne=(ce=ce.getDenom().group===St?pt.expand(ce):ce).stripVar(n),re=pt.divide(ce.clone(),ne.clone());if(ne.contains(n)&&(re=pt.multiply(re,ne),ne=new dt(1)),re.group!==Et){if(re.equals(1))return Vt.integrate(pt.expand(ce),n,ut);re.clone().toLinear().isPoly(!0)&&1<ct.Utils.variables(re).length&&(re=ct.Algebra.Factor.factor(re)),t=Vt.integrate(re,n,ut)}else{var ie=re.collectSymbols().sort(function(e,t){return e.group===t.group?Number(e.power)===Number(t.power)?e<t?1:-1:t.power-e.power:t.group-e.group}).map(function(e){e=dt.unwrapSQRT(e,!0);return"exp"===e.fname?pt.parse(yt("({1})*e^({0})",e.args[0],e.multiplier)):e}),se=ie.length;if(ce.power<0){if(2===se)return Vt.integrate(pt.expand(ce),n,ut,lt)}else if(2===se){try{t=Vt.integration.u_substitution(ie,n)}catch(e){}if(!t){var oe,ae,ue,le,ce,pe,fe,he,me,ge,de,ve,we,ye,be,Se,Me,Ne,Ee,qe,xe,Ae,Ce,Le,Ie,Ue,_e,Re,Oe,Te,Pe=ie[0].group,ke=ie[1].group,Fe=ie[0],De=ie[1],Be=Fe.fname,Ge=De.fname;if(ce=pt.multiply(Fe.clone(),De.clone()),Pe===gt&&ke===gt)if(Be===xt||Ge===xt)t=Vt.integration.by_parts(ce.clone(),n,ut,lt);else{ie.sort(function(e,t){return t.fname>e.fname});var Ve,He=Fe.args[0];He.isLinear()&&(He.group===Nt||He.group===Et||He.group===St)||Vt.integration.stop(),h=(Ve=Vt.integration.decompose_arg(He,n))[1],f=Ve[0],h.isLinear()||Vt.integration.stop();var je,Ze=De.args[0];if(He.equals(Ze))if(Be===Ct&&Ge===Lt||Be===Lt&&Ge===Ct)if(Fe.power.lessThan(0)&&Vt.integration.stop(),Be===Ct&&Fe.power.add(De.power).equals(0))Fe.fname=It,Fe.updateHash(),t=Vt.integrate(Fe,n,ut);else if(bt(Fe.power)&&Ge===Lt&&De.power.lessThan(0)){var _=Number(Fe.power)/2,Xe=pt.parse(yt("(1-cos({0})^2)^({1})",Fe.args[0],_));t=Vt.integrate(pt.expand(pt.multiply(Xe,De.clone())),n,ut,lt)}else if(bt(Fe.power)&&Ge===Ct&&De.power.lessThan(0)){_=Number(Fe.power)/2,Xe=pt.parse(yt("(1-sin({0})^2)^({1})",Fe.args[0],_));t=Vt.integrate(pt.expand(pt.multiply(Xe,De.clone())),n,ut,lt)}else{var $e,ze=ct.Utils.even(Fe.power),Qe=ct.Utils.even(De.power);if(t=new dt(0),ze&&Qe){var Ye=function(e){var t=e.power/2,t=e.fname===Lt?"((1/2)+(cos(2*("+e.args[0]+"))/2))^"+t:"((1/2)-(cos(2*("+e.args[0]+"))/2))^"+t;return pt.parse(t)},f=Ye(Fe),c=Ye(De),We=pt.multiply(f,c);return(Je=pt.expand(We)).each(function(e){t=pt.add(t,Vt.integrate(e,n,ut))}),pt.multiply(t,ne)}nt=ze?($e=Fe,De):($e=De,Fe);var Je,Ke=$e.fname===Lt?-1:1,et=((_=nt.power)-1)/2,tt=pt.parse("(1-"+$e.fname+ct.Utils.inBrackets(He)+"^2)^"+et);(Je=pt.expand(pt.multiply(new dt(Ke),pt.multiply($e.clone(),tt)))).each(function(e){t=pt.add(t,Vt.integration.poly_integrate(e.clone()))})}else Be===Ut&&Ge===It&&h.isLinear()&&De.isLinear()?t=pt.parse(yt("sec({0})^({1})/({1})",Fe.args[0],Fe.power)):Be===It&&Ge===Ut&&h.isLinear()?Fe.isLinear()&&De.isLinear()?t=pt.divide(pt.symfunction(Ut,[He.clone()]),f):bt(Fe.power)?(s=Number(Fe.power)/2,We=pt.parse(yt("(sec({0})^2-1)^({1})",Fe.args[0],s)),t=Vt.integrate(pt.expand(pt.multiply(We,De)),n,ut)):Vt.integration.stop():t=Be===Ut&&Ge===Lt?(Fe.fname=Lt,Fe.invert().updateHash(),Vt.integrate(pt.multiply(Fe,De),n,ut)):Be===Ct&&Ge===_t?(De.fname=Ct,De.invert().updateHash(),Vt.integrate(pt.multiply(Fe,De),n,ut)):(We=Be!==It||Ge!==Lt&&Ge!==Ct||!De.power.lessThan(0)?pt.multiply(Fe.fnTransform(),De.fnTransform()):pt.multiply(Fe.fnTransform(),De),Vt.integrate(pt.expand(We),n,ut));else Be!==Ct&&Be!==Lt||Ge!==Ct&&Ge!==Lt?Vt.integration.stop():Fe.isLinear()&&De.isLinear()?t=Fe.args[0].isLinear()&&De.args[0].isLinear()?(Ge===Ct?(p=Fe.args[0],je=De.args[0]):(je=Fe.args[0],p=De.args[0]),O=pt.parse(yt("(sin(({1})+({0}))+sin(({1})-({0})))/2",p.toString(),je.toString())),Vt.integrate(O,n,ut)):(st=Gt(ie),Vt.integrate(pt.expand(st),n,ut)):(st=new dt(1),ie.map(function(e){e=e.fnTransform();st=pt.multiply(st,e)}),We=pt.expand(st),(t=Vt.integrate(We,n,ut)).hasIntegral()&&(t=Vt.integrate(Gt(st.collectSymbols()),n,ut)))}else Pe===gt&&ke===St?(oe=Fe.isLinear(),Fe.fname===Lt&&oe&&De.power.equals(-1)?t=pt.symfunction("Ci",[Fe.args[0]]):Fe.fname===Lt&&De.power.equals(-1)?t=Vt.integrate(pt.multiply(Fe.fnTransform(),De.clone()),n,ut):Fe.fname===kt&&oe&&De.power.equals(-1)?t=pt.symfunction("Chi",[Fe.args[0]]):Fe.fname===kt&&De.power.equals(-1)?t=Vt.integrate(pt.multiply(Fe.fnTransform(),De.clone()),n,ut):Fe.fname===Ct&&oe&&De.power.equals(-1)?t=pt.symfunction("Si",[Fe.args[0]]):Fe.fname===Ct&&De.power.equals(-1)?t=Vt.integrate(pt.multiply(Fe.fnTransform(),De.clone()),n,ut):Fe.fname===Pt&&oe&&De.power.equals(-1)?t=pt.symfunction("Shi",[Fe.args[0]]):Fe.fname===Pt&&De.power.equals(-1)?t=Vt.integrate(pt.multiply(Fe.fnTransform(),De.clone()),n,ut):Fe.fname===xt&&De.power.equals(-1)?t=Vt.integration.poly_integrate(Fe,n,ut):"erf"===Fe.fname?De.power.equals(1)&&(ee=(Se=Vt.integration.decompose_arg(Fe.args[0],n))[0],K=Se[1],D=Fe.args[0].toString(),t=pt.parse(yt("(e^(-(({2}))^2)*(sqrt(pi)*e^((({2}))^2)*(2*({0})^2*({1})^2-3)*erf(({2}))+2*({0})*({1})-2))/(4*sqrt(pi)*({0})^2)",ee,K,D))):t=Vt.integration.by_parts(ce,n,ut,lt)):Pe===qt&&ke===St?(h=Be===xt?Vt.integration.decompose_arg(Fe.args[0],n)[1]:null,t=Fe.isE()&&(Fe.power.group===St||Fe.power.group===Et)&&De.power.equals(-1)?pt.symfunction("Ei",[Fe.power.clone()]):Be===xt&&h.value===De.value?Vt.integration.poly_integrate(Fe,n,ut):Vt.integration.by_parts(ce,n,ut,lt)):Pe===Mt&&ke===St?(ce=De.value===Fe.value&&Fe.power.equals(-1)?(ae=Math.min.apply(null,ct.Utils.keys(Fe.symbols)),ue=Math.min(ae,De.power),(le=De.clone()).power=new ft(ue),De=pt.divide(De,le.clone()),We=new dt(0),Fe.each(function(e){We=pt.add(We,pt.divide(e.clone(),le.clone()))}),We.multiplier=Fe.multiplier,pt.divide(De,We)):pt.expand(ce),t=Vt.integration.partial_fraction(ce,n,ut)):Pe===Nt&&ke===St?(O=Fe.clone().toLinear(),pe=ct.Algebra.degree(O,pt.parse(n)).equals(1),Fe.power.equals(-.5)?(f=(Ve=Vt.integration.decompose_arg(Fe.clone().toLinear(),n))[0].negate(),h=Ve[1],c=Ve[3],xe=Number(Fe.power),Ae=Number(De.power),wt(Ae)&&ct.Utils.even(Ae)&&h.power.equals(2)?(Me=pt.divide(pt.multiply(pt.pow(c.clone(),new dt(2)),pt.symfunction(At,[pt.divide(c.clone(),f.clone())])),pt.pow(f.clone(),new dt(2))),Me=pt.multiply(Me,pt.symfunction(At,[c]).invert()),(fe=pt.parse("sin(u)")).power=fe.power.multiply(De.power),R=Vt.integrate(fe,"u",ut),he=pt.parse("asin(sqrt("+f+"/"+c+")*"+n+")"),t=pt.multiply(Me,R.sub(new dt("u"),he))):-.5===xe&&(me=function(e,t){t=pt.parse(Vt.integrate(e,n,ut,lt).sub(n,yt(t,n)));if(!t.hasIntegral())return t},-1===Ae?t=me(pt.expand(pt.expand(pt.pow(pt.multiply(Fe.invert(),De.invert()),new dt(2)))).invert(),"sqrt(1-1/({0})^2)"):-2===Ae&&(t=me(pt.sqrt(pt.expand(pt.divide(pt.pow(ce,new dt(2)).invert(),pt.pow(new dt(n),new dt(2))).negate())).invert(),"sqrt(1-1/({0})^2)")))):Fe.power.equals(-1)&&De.isLinear()&&pe?t=Vt.integration.partial_fraction(ce,n,ut):!Fe.power.lessThan(0)&&wt(Fe.power)?(ge=pt.expand(Fe),t=new dt(0),ge.each(function(e){e.group===Mt?e.each(function(e){t=pt.add(t,Vt.integrate(pt.multiply(De.clone(),e),n,ut))}):t=pt.add(t,Vt.integrate(pt.multiply(De.clone(),e),n,ut))})):Fe.power.lessThan(-2)?t=Vt.integration.by_parts(ce,n,ut,lt):Fe.power.lessThan(0)&&De.power.greaterThan(1)?(f=(Ve=Vt.integration.decompose_arg(Fe.clone().toLinear(),n))[0].negate(),h=Ve[1],c=Ve[3],l=Fe.clone().toLinear(),t=h.group!==Mt&&h.isLinear()?(s=Number(De.power),$e=new dt(Ce="_u_"),de=pt.expand(pt.divide(pt.pow(pt.subtract($e.clone(),c.clone()),new dt(s)),$e.clone())),(ve={})[Ce]=l,we=pt.parse(de,ve),Vt.integrate(we,n,0)):De.power.greaterThan(h.power)||De.power.equals(h.power)?(ye=new ct.Algebra.Classes.Factors,Fe=ct.Algebra.Factor.coeffFactor(Fe.invert(),ye),(be=ct.Algebra.divide(De,Fe)).group!==Et?(t=new dt(0),be.each(function(e){t=pt.add(t,Vt.integrate(e,n,ut))}),ye.each(function(e){t=pt.divide(t,e)}),pt.expand(t)):Vt.integration.by_parts(ce,n,ut,lt)):Vt.integration.partial_fraction(ce,n,ut)):Fe.power.den.equals(2)?(f=(Se=Vt.integration.decompose_arg(Fe.clone().toLinear(),n))[3],h=Se[1],c=Se[0],je=Se[2],t=h.power.equals(2)&&c.lessThan(0)?(f.equals(1)||(ne=pt.multiply(ne,pt.pow(f,new dt(2)))),$e=n,Me=pt.divide(pt.pow(c.clone().negate(),new dt(.5)),pt.pow(f,new dt(.5))),Ce=pt.symfunction(Lt,[new dt($e)]),Ne=pt.pow(pt.symfunction(Lt,[new dt($e)]),new dt(Fe.power.num)),Ee=pt.pow(pt.symfunction(Ct,[new dt($e)]),new dt(De.power)),qe=pt.multiply(pt.multiply(Ne,Ce),Ee),(R=Vt.integrate(qe,$e,ut)).sub($e,pt.symfunction(Ot,[pt.multiply(new dt(n),Me)]))):Vt.integration.partial_fraction(ce,n,ut,lt)):pe&&(t=Vt.integration.partial_fraction(ce,n,ut))):Fe.isComposite()&&De.isComposite()?(t=new dt(0),Fe.power.greaterThan(0)&&De.power.greaterThan(0)?(Je=pt.expand(ce)).each(function(e){t=pt.add(t,Vt.integrate(e,n,ut))},!0):(xe=Number(Fe.power),Ae=Number(De.power),xe<0&&0<Ae&&(We=Fe,Fe=De,De=We),-1===xe&&-1===Ae?t=Vt.integration.partial_fraction(ce,n):Fe.each(function(e){e=pt.multiply(e,De.clone()),e=Vt.integrate(e,n,ut);t=pt.add(t,e)}))):Pe===Nt&&ie[0].power.greaterThan(0)?(Fe=pt.expand(Fe),t=new dt(0),Fe.each(function(e){t=pt.add(t,Vt.integrate(pt.multiply(e,De.clone()),n,ut))},!0)):Pe===gt&&ke===qt&&ct.Utils.in_htrig(Fe.fname)?(Fe=Fe.fnTransform(),t=Vt.integrate(pt.expand(pt.multiply(Fe,De)),n,ut)):Pe===gt&&ke===Nt||ke===gt&&Pe===Nt?(ke===gt&&Pe===Nt&&(We=Fe,Fe=De,De=We),Ce=dt.unwrapSQRT(Vt.diff(Fe.clone(),n),!0),Le=dt.unwrapSQRT(De,!0),Ce.power.equals(Le.power)?(s=new dt(De.power),Ue=Ce.clone().toLinear(),_e=De.clone().toLinear(),(Ie=ct.Algebra.divide(Ue.toLinear(),_e)).isConstant()&&(Re=pt.pow(Ie,s.negate()),t=pt.multiply(Re,Vt.integration.poly_integrate(Fe.clone())))):t=Vt.integration.by_parts(ce,n,ut,lt)):(Oe=Fe.clone().toLinear(),Te=De.clone().toLinear(),t=Pe===qt&&ke===qt&&Fe.power.contains(n)&&De.power.contains(n)&&!Oe.contains(n)&&!Te.contains(n)?pt.parse(yt("(({0})^(({2})*({4}))*({1})^(({3})*({4})))/(log(({0})^({2}))+log(({1})^({3})))",Oe.toString(),Te.toString(),Fe.power.multiplier.toString(),De.power.multiplier.toString(),n)):Vt.integration.by_parts(ce,n,ut,lt))}}else if(3===se&&(ie[2].group===St&&ie[2].power.lessThan(2)||ie[0].group===Nt)){var nt,rt=ie[0];rt.group===Nt?(rt.power.greaterThan(1)&&(rt=pt.expand(rt)),nt=pt.multiply(ie[1],ie[2]),t=new dt(0),rt.each(function(e){e=pt.multiply(e,nt.clone()),e=Vt.integrate(e,n,ut);t=pt.add(t,e)},!0)):t=Vt.integration.by_parts(ce,n,ut,lt)}else if(Bt(ie)){for(var We=new dt(1),it=0,se=ie.length;it<se;it++)We=pt.multiply(We,ie[it].fnTransform());We=pt.expand(We),t=Vt.integrate(We,n,ut)}else{var st=Gt(ie);t=Vt.integrate(pt.expand(st),n,ut)}}t=pt.multiply(t,ne)}}else t=pt.multiply(ce.clone(),pt.parse(n));if(t)return t}catch(e){if(!(e instanceof Dt||e instanceof ct.exceptions.DivisionByZero))throw e}return pt.symfunction("integrate",[ot,at])},!1))},defint:function(e,t,n,r){r=r||"x";function i(t,e,n){try{return pt.parse(t,e)}catch(e){return Vt.Limit.limit(t,r,n)}}var s,o,a=ct.Utils.variables(e),u=e.hasTrig();return 1!==a.length||r||(r=a[0]),u||(s=Vt.integrate(e,r)),u||s.hasIntegral()?1===a.length&&t.isConstant()&&n.isConstant()?(o=ct.Utils.build(e),new dt(ct.Math2.num_integrate(o,Number(t),Number(n)))):pt.symfunction("defint",[e,t,n,r]):(o={},(e={})[r]=n,o[r]=t,n=i(s,e,n),t=i(s,o,t),pt.subtract(n,t))},Limit:{interval:function(e,t){return pt.parse(yt("[{0}, {1}]",e,t))},diverges:function(){return 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F,D=se.rewrite(c,null,p),P=D[0],k=D[1];if(P.group===ee)"abs"===P.fname?o([k.clone(),k.negate()]):"sin"===P.fname?o(se.inverseFunctionSolve("asin",P,k)):"cos"===P.fname?o(se.inverseFunctionSolve("acos",P,k)):"tan"===P.fname?o(se.inverseFunctionSolve("atan",P,k)):P.fname===G.Settings.LOG?(y=(F=Z(P.args[0],p))[1]).group===Y&&(c=new re(y,k=V.divide(V.subtract(V.pow(1<P.args.length?P.args[1]:new z("e"),V.divide(k,V.parse(P.multiplier))),F[3]),F[0])).toLHS(),o(oe(c,p))):o(V.subtract(P,k));else{var B=new re(P,k).toLHS();if(B.equals(c))throw new Error("Stopping. 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u=n.power.stripVar(r);o=A.parse(L("1/(({1})-({0}))",u,i))}return A.multiply(o,e)},inverse:function(M,N,E){var q=M.clone();return x.Utils.block("POSITIVE_MULTIPLIERS",function(){if((M=M.group===_?x.Algebra.PartFrac.partfrac(A.expand(M),N):M).group===I||M.group===_||M.isComposite()){var e,t,n,r,i,s,o,a,u,l,c,p,f,h,m,g=function(){(s=A.multiply(s,e)).multiplier=s.multiplier.multiply(M.multiplier),s=A.divide(s,r.a)},d=M.multiplier.clone();if(M.toUnitMultiplier(),e=M.getNum(),(t=M.getDenom().toUnitMultiplier()).group===U?(i=t.power.clone(),t.toLinear()):i=new x.Frac(1),n=N.toString(),r=x.Utils.decompose_fn(t,n,!0),x.Utils.decompose_fn(A.expand(e.clone()),n,!0),e.multiplier=e.multiplier.multiply(d),(t.group===I||t.group===_)&&r.x.value===n&&r.b.equals(0)&&x.Utils.isInt(r.x.power))p=r.x.power-1,f=x.Math2.factorial(p),s=A.divide(A.pow(E,new C(p)),new C(f)),g();else 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C(1),e.each(function(e){e.contains(n)?o=A.multiply(o,e):h=A.multiply(h,e)}),e=o),u=(a=x.Utils.decompose_fn(e,n,!0)).a,l=a.b,c=u.containsFunction("sin"),p=u.containsFunction("cos"),f=l.containsFunction("cos"),g=l.containsFunction("sin"),a.x.value===n&&a.x.isLinear()&&!(c&&f||p||g)?s=A.parse(L("(({1})*cos((sqrt(({2})*({3}))*({0}))/({2})))/({2})",E,a.a,r.a,r.b)):c&&f&&(c=u.findFunction("sin"),f=l.findFunction("cos"),c.args[0].equals(f.args[0])&&!c.args[0].contains(n)&&(v=A.divide(l,f.toUnitMultiplier()).toString(),f=c.args[0].toString(),m=r.b,c=A.divide(u,c.toUnitMultiplier()),s=A.parse(L("(({1})*({2})*cos({3})*sin(sqrt({4})*({0})))/sqrt({4})+({1})*sin({3})*({5})*cos(sqrt({4})*({0}))",E,h,v,f,m,c))))):s=A.parse(L("(({1})*sin((sqrt(({2})*({3}))*({0}))/({2})))/sqrt(({2})*({3}))",E,e,r.a,r.b)));else if(r.x.power.num&&r.x.power.num.equals(3)&&r.x.power.den.equals(2)&&e.contains("sqrt(pi)")&&!e.contains(n)&&e.isLinear()){var v=A.divide(e.clone(),A.parse("sqrt(pi)"));s=A.parse(L("(2*({2})*sqrt({0}))/({1})",E,r.a,v,e))}else if(i.equals(2)&&r.x.power.equals(2))if(e.contains(n))if((a=x.Utils.decompose_fn(A.expand(e.clone()),n,!0)).x.isComposite()){var w=[],y=e.collectSymbols(function(e){e=C.unwrapPARENS(e);var t=x.Utils.decompose_fn(e,n,!0);return t.symbol=e,t}).sort(function(e,t){e=e.x.value!==n?0:e.x.power;return(t.x.value!==n?0:t.x.power)-e});h=new C(-1);for(var b=0;b<y.length;b++){var S=y[b];S.x.value===n?w.push(S):h=A.multiply(h,S.symbol)}w[0].x.power.equals(2)&&w[1].x.power.equals(1)&&w[1].b.equals(0)&&!w[0].b.equals(0)&&(v=w[0].a.negate(),s=A.parse(L("-(({1})*({2})*({5})*({0})*sin((sqrt(({4})*({5}))*({0}))/({4})))/(2*({4})^2*sqrt(({4})*({5})))-(({1})*({3})*({0})*sin((sqrt(({4})*({5}))*({0}))/({4})))/(2*({4})*sqrt(({4})*({5})))+(({1})*({2})*cos((sqrt(({4})*({5}))*({0}))/({4})))/({4})^2",E,h,v,w[0].b,r.a,r.b)))}else a.x.isLinear()?(h=A.divide(a.a,new C(2)),s=A.parse(L("(({1})*({0})*sin((sqrt(({2})*({3}))*({0}))/({2})))/(({2})*sqrt(({2})*({3})))",E,h,r.a,r.b))):a.x.power.equals(2)&&(s=a.b.equals(0)?(h=A.divide(a.a,new C(2)),A.parse(L("(({1})*sin((sqrt(({2})*({3}))*({0}))/({2})))/(({2})*sqrt(({2})*({3})))+(({1})*({0})*cos((sqrt(({2})*({3}))*({0}))/({2})))/({2})^2",E,h,r.a,r.b))):(h=A.divide(a.a,new C(2)),m=a.b.negate(),A.parse(L("-((({2})*({4})-2*({1})*({3}))*sin((sqrt(({2})*({3}))*({0}))/({2})))/(2*({2})*({3})*sqrt(({2})*({3})))+(({4})*({0})*cos((sqrt(({2})*({3}))*({0}))/({2})))/(2*({2})*({3}))+(({1})*({0})*cos((sqrt(({2})*({3}))*({0}))/({2})))/({2})^2",E,h,r.a,r.b,m))));else h=A.divide(e,new C(2)),s=A.parse(L("(({1})*sin((sqrt(({2})*({3}))*({0}))/({2})))/(({3})*sqrt(({2})*({3})))-(({1})*({0})*cos((sqrt(({2})*({3}))*({0}))/({2})))/(({2})*({3}))",E,h,r.a,r.b));else M.isComposite()&&(i.equals(2)&&r.x.group===I?s=A.parse(`(${d})*(${E})*e^(-(${r.b})*(${E}))`):(s=new C(0),M.each(function(e){s=A.add(s,R.LaPlace.inverse(e,N,E))},!0)))}return s=s||A.symfunction("ilt",[q,N,E])},!0)}},Statistics:{frequencyMap:function(e){for(var t={},n=0,r=e.length;n<r;n++){var i=e[n].toString();t[i]||(t[i]=0),t[i]++}return t},sort:function(e){return e.sort(function(e,t){return e.isConstant()&&t.isConstant()||A.error("Unable to sort! 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ID : 3 & Title : Static Equilibrium and Triangle of Forces , Pulleys and Three Weights
let m1=50; let m2=50; let m3=60; let E1= `${m1}*cos(A)-${m3}*cos(B)=0`; let E2= `${m1}*sin(A)+${m3}*sin(B)=${m2}`; let E = nerdamer.solveEquations([E1,E2]); let A = Make360(RadToDeg(E[0][1])); let B = Make360(RadToDeg(E[1][1])); while(A>90){ A=180-A;}; while(B>90){ B=180-B;}; B=180-B
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Number of ID : 3