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Integrate a polynomial beside a sine of a power of a shifted linear in that linear #2095

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Merged
Rafael-SOWNet merged 1 commit into from
Oct 23, 2026
Merged

Integrate a polynomial beside a sine of a power of a shifted linear in that linear #2095

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12 changes: 9 additions & 3 deletions Sources/AngouriMath/Functions/Continuous/Integration/IndefiniteIntegralSolver.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -18385,7 +18385,8 @@ private static (Entity Logarithm, Entity Degree, Entity Offset, Entity Slope)? T

/// <summary>
/// Whether <paramref name="factor"/> is a power that is not whole of something holding a logarithm of something in
/// <paramref name="x"/>, or an exponential of something in <paramref name="x"/> that is not linear in it.
/// <paramref name="x"/>, an exponential of something in <paramref name="x"/> that is not linear in it, or holds a
/// sine or a cosine of one.
/// </summary>
private static bool IsATranscendentalPowerOfSomethingInX(Entity factor, Entity.Variable x) => factor switch
{
Expand All @@ -18394,8 +18395,13 @@ private static (Entity Logarithm, Entity Degree, Entity Offset, Entity Slope)? T
=> exponent.Nodes.Any(node => node is Sumf or Minusf && node.ContainsNode(x))
&& !TreeAnalyzer.TryGetPolyLinear(exponent, x, out _, out _),
Powf(var @base, var exponent) when !exponent.ContainsNode(x) && exponent is not Number.Integer
=> @base.Nodes.Any(node => node is Logf(_, var antilogarithm) && antilogarithm.ContainsNode(x)),
_ => false
&& @base.Nodes.Any(node => node is Logf(_, var antilogarithm) && antilogarithm.ContainsNode(x)) => true,
// A sine or a cosine of a sum in x that is not linear, in whatever holds it: x sin(a + b (c + d x)^3), and
// x (a + b sin(c + d (f + g x)^n))^2, which in u are powers of u beside the sine of a power of u, Euler's
// formula's exponentials. Rubi's 4.1.12.
_ => factor.Nodes.Any(node => node is Sinf or Cosf && node.DirectChildren.First() is var argument && argument.ContainsNode(x)
&& argument.Nodes.Any(inner => inner is Sumf or Minusf && inner.ContainsNode(x))
&& !TreeAnalyzer.TryGetPolyLinear(argument, x, out _, out _))
};

/// <summary>
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9 changes: 7 additions & 2 deletions Sources/Tests/UnitTests/Calculus/APowerBesideAnExponentialOfAPowerIntegralTest.cs
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Expand Up @@ -126,14 +126,19 @@ public void APositiveRateIsTakenOutOfThePower()

/// <summary>
/// A polynomial beside a symbolic power of a logarithm of one shifted linear, or an exponential of a power of one,
/// written in <c>u = a + b x</c>, where each term is a gamma function. The constant in front comes along. Rubi's 3.3,
/// 3.4 and 2.3.
/// written in <c>u = a + b x</c>, where each term is a gamma function. The constant in front comes along. And beside
/// a sine or a cosine of a power of one, which in u is Euler's formula's exponentials of a power of u. Rubi's 3.3,
/// 3.4, 2.3 and 4.1.12.
/// </summary>
[Theory]
[InlineData("2*x*(a + b*ln(c*(d + f*x)))^n")]
[InlineData("x*(a + b*ln(c*(d + f*sqrt(x))))^n")]
[InlineData("x^2*f^(c*(a + b*x)^3)")]
[InlineData("(a + b*x)^2*e^(-c*(d + f*x)^3)")]
[InlineData("(a + f*x)*sin(b + c*(d + f*x)^3)")]
[InlineData("x*sin(a + b*(c + d*x)^n)")]
[InlineData("x^2*cos(a + b/(c + d*x)^3)")]
[InlineData("x*(a + b*sin(c + d*(f + x)^n))^2")]
public void APolynomialBesideAFunctionOfAShiftedLinear(string integrand) => DifferentiatesBack(integrand);

/// <summary>
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