halirutan

import org.gradle.api.internal.ConventionTask

buildscript {
  repositories {
    mavenCentral()
  }
  dependencies {
    classpath("de.undercouch:gradle-download-task:4.0.2")
  }
}

halirutan

/*
 * Copyright (c) 2018 Patrick Scheibe
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *

halirutan

/*
 * Copyright (c) 2017 Patrick Scheibe
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in

halirutan

/*
 * Copyright (c) 2018 Patrick Scheibe
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *

halirutan

\[Aleph];
\[Alpha];
\[And];
\[Angle];
\[Angstrom];
\[AscendingEllipsis];
\[Backslash];
\[BeamedEighthNote];
\[BeamedSixteenthNote];
\[Because];

halirutan

halirutan

Two months ago, Albert Rich posted "What's the hardest integral Mathematica running Rubi can find?" here on the Wolfram Community. You might have also seen that I answered in detail and pointed out the things that could help to improve Rubi. While it appears nothing really happened afterward, this is far from reality. Since then, Albert and I have worked closely together to make Rubi more accessible. If you like to read about how this all started, let me invite you to read my latest blog-post about our collaboration. However, here, we want to share an update that should serve as an overview of what we have done to improve Rubi.

First of all, Rubi has got a new home under rulebasedintegration.org and Albert's old site will no longer be updated. On the new website, you will find information, installation instructions, and links to the source-code and test-suites.

halirutan

Int[Times[Optional[Pattern[u, Blank[]]], Power[Plus[Pattern[a, Blank[]], Times[Optional[Pattern[b, Blank[]]], Power[Pattern[x, Blank[]], Optional[Pattern[n, Blank[]]]]]], Optional[Pattern[p, Blank[]]]]], Pattern[x, Blank[Symbol]]] := Int[u*(b*x^n)^p, x] /; FreeQ[{a, b, n, p}, x] && EqQ[a, 0]
Int[Times[Optional[Pattern[u, Blank[]]], Power[Plus[Optional[Pattern[a, Blank[]]], Times[Optional[Pattern[b, Blank[]]], Power[Pattern[x, Blank[]], Optional[Pattern[n, Blank[]]]]]], Optional[Pattern[p, Blank[]]]]], Pattern[x, Blank[Symbol]]] := Int[u*a^p, x] /; FreeQ[{a, b, n, p}, x] && EqQ[b, 0]
Int[Times[Optional[Pattern[u, Blank[]]], Power[Plus[Pattern[a, Blank[]], Times[Optional[Pattern[c, Blank[]]], Power[Pattern[x, Blank[]], Optional[Pattern[j, Blank[]]]]], Times[Optional[Pattern[b, Blank[]]], Power[Pattern[x, Blank[]], Optional[Pattern[n, Blank[]]]]]], Optional[Pattern[p, Blank[]]]]], Pattern[x, Blank[Symbol]]] := Int[u*(b*x^n + c*x^(2*n))^p, x] /; FreeQ[{a, b, c, n, p}, x] && EqQ[j, 2*n] && EqQ[a, 0]
Int[Times[Opti

halirutan

// {Sqrt[1 + 2*x], x, 1, (1 + 2*x)^(3/2)/3}
public void test00001() {
	check("Integrate[Sqrt[1 + 2*x], x]", "(1 + 2*x)^(3/2)/3");

}

// {(1 + x)/(2 + 2*x + x^2)^3, x, 1, -1/(4*(2 + 2*x + x^2)^2)}
public void test00002() {
	check("Integrate[(1 + x)/(2 + 2*x + x^2)^3, x]", "-1/(4*(2 + 2*x + x^2)^2)");

halirutan

Int[(u_.)*((a_) + (b_.)*(x_)^(n_.))^(p_.), x_Symbol] := Int[u*(b*x^n)^p, x] /; FreeQ[{a, b, n, p}, x] && EqQ[a, 0]
Int[(u_.)*((a_.) + (b_.)*(x_)^(n_.))^(p_.), x_Symbol] := Int[u*a^p, x] /; FreeQ[{a, b, n, p}, x] && EqQ[b, 0]
Int[(u_.)*((a_) + (c_.)*(x_)^(j_.) + (b_.)*(x_)^(n_.))^(p_.), x_Symbol] := Int[u*(b*x^n + c*x^(2*n))^p, x] /; FreeQ[{a, b, c, n, p}, x] && EqQ[j, 2*n] && EqQ[a, 0]
Int[(u_.)*((a_.) + (c_.)*(x_)^(j_.) + (b_.)*(x_)^(n_.))^(p_.), x_Symbol] := Int[u*(a + c*x^(2*n))^p, x] /; FreeQ[{a, b, c, n, p}, x] && EqQ[j, 2*n] && EqQ[b, 0]
Int[(u_.)*((a_.) + (c_.)*(x_)^(j_.) + (b_.)*(x_)^(n_.))^(p_.), x_Symbol] := Int[u*(a + b*x^n)^p, x] /; FreeQ[{a, b, c, n, p}, x] && EqQ[j, 2*n] && EqQ[c, 0]
Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] := Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x] &&  !FreeQ[v, x]
Int[(u_.)*(Px_)^(p_), x_Symbol] := Int[u*Px^Simplify[p], x] /; PolyQ[Px, x] &&  !RationalQ[p] && FreeQ[p, x] && RationalQ[Simplify[p]]
Int[a_, x_Symbol] := Simp[a*x, x] /; FreeQ[a, x]
Int[