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SolveByTheReciprocalOfAFunctionOfTheReciprocal(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)

Method (no overloads)

Summary

A rational function of x and of trigonometric functions of a + b/x, under
x = 1/u: sin(c + d/x)/(e + f x) is
-sin(c + d u)/(u (e u + f)) du, which the partial fractions and the sine and
cosine integrals answer.

Remarks

x = 1/u is one-to-one on either side of 0, so the answer in u written back
in 1/x holds on both. Every argument of a function holding x has to be
linear in 1/x and not in x, so the integrand in u is one this rule
does not read again. Rubi's 4.1.12 (a + b sin(c + d/x))^k/(e + f x)^m were
declined: the substitution search reads a candidate's derivative but never solves
the candidate for x. https://github.com/asc-community/AngouriMath/issues/718

AngouriMath

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AngouriMath

SolveByTheReciprocalOfAFunctionOfTheReciprocal​(AngouriMath.​Entity,​AngouriMath.​Entity.​Variable,​System.​Boolean)

SolveByTheReciprocalOfAFunctionOfTheReciprocal(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)