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IsDifferentiatedBeforeAPolynomial(AngouriMath.Entity)

Method (no overloads)

Summary

Whether factor is one of the functions integration by parts
differentiates rather than integrates when the other factor is a polynomial.

Remarks

This is the L and the I of LIATE, which both come before A. The
rule below implemented only the L, and the reason it gives for the logarithm is the
same one that holds for an inverse trigonometric function: differentiating it turns it
into something algebraic that cancels against the integrated polynomial and ends,
where integrating it puts the original integral back in front of us.
x * atan(x) is the case: differentiating atan gives 1/(1 + x^2) and what is left is x^2/(2(1 + x^2)), which is answered; integrating it first
gives an antiderivative holding x*atan(x) again, which is where the search went
instead and why it was left unevaluated.
The special functions belong here for the same reason, since each has an elementary
derivative: x Ei(b x) leaves x e^(b x)/2 after one step, and
x^2 Si(b x) leaves x^2 sin(b x)/3, where integrating the special function
first gives an antiderivative that holds it again.
https://github.com/asc-community/AngouriMath/issues/1501
https://github.com/asc-community/AngouriMath/issues/718

AngouriMath

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AngouriMath

IsDifferentiatedBeforeAPolynomial​(AngouriMath.​Entity)

IsDifferentiatedBeforeAPolynomial(AngouriMath.Entity)