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node_modules/fraction.js/examples/integrate.js

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+/*
+Fraction.js v5.0.0 10/1/2024
+https://raw.org/article/rational-numbers-in-javascript/
+
+Copyright (c) 2024, Robert Eisele (https://raw.org/)
+Licensed under the MIT license.
+*/
+const Fraction = require('fraction.js');
+
+// NOTE: This is a nice example, but a stable version of this is served with Polynomial.js: 
+// https://github.com/rawify/Polynomial.js
+
+function integrate(poly) {
+
+    poly = poly.replace(/\s+/g, "");
+
+    var regex = /(\([+-]?[0-9/]+\)|[+-]?[0-9/]+)x(?:\^(\([+-]?[0-9/]+\)|[+-]?[0-9]+))?/g;
+    var arr;
+    var res = {};
+    while (null !== (arr = regex.exec(poly))) {
+
+        var a = (arr[1] || "1").replace("(", "").replace(")", "").split("/");
+        var b = (arr[2] || "1").replace("(", "").replace(")", "").split("/");
+
+        var exp = new Fraction(b).add(1);
+        var key = "" + exp;
+
+        if (res[key] !== undefined) {
+            res[key] = { x: new Fraction(a).div(exp).add(res[key].x), e: exp };
+        } else {
+            res[key] = { x: new Fraction(a).div(exp), e: exp };
+        }
+    }
+
+    var str = "";
+    var c = 0;
+    for (var i in res) {
+        if (res[i].x.s !== -1n && c > 0) {
+            str += "+";
+        } else if (res[i].x.s === -1n) {
+            str += "-";
+        }
+        if (res[i].x.n !== res[i].x.d) {
+            if (res[i].x.d !== 1n) {
+                str += res[i].x.n + "/" + res[i].x.d;
+            } else {
+                str += res[i].x.n;
+            }
+        }
+        str += "x";
+        if (res[i].e.n !== res[i].e.d) {
+            str += "^";
+            if (res[i].e.d !== 1n) {
+                str += "(" + res[i].e.n + "/" + res[i].e.d + ")";
+            } else {
+                str += res[i].e.n;
+            }
+        }
+        c++;
+    }
+    return str;
+}
+
+var poly = "-2/3x^3-2x^2+3x+8x^3-1/3x^(4/8)";
+
+console.log("f(x): " + poly);
+console.log("F(x): " + integrate(poly));