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

 Method (no overloads)

Summary

x^m (a + b atan(c x))^p over a power of d (1 +- i c x), under x = tan(u)/c, where
1 + i tan(u) is e^(i u)/cos(u): the integrand in u is
(a + b u)^p (tan(u)/c)^m d^(-k) e^(-+i k u) cos(u)^k/(c cos(u)^2), a polynomial in u times
exponentials and trigonometric functions, and the answer is written back at u = atan(c x).

Remarks

1 + i tan(u) = (cos(u) + i sin(u))/cos(u) holds for every u where the tangent is defined,
and atan(c x) takes each real x into (-pi/2, pi/2), where it is. Rubi's 5.3.4
(a + b atan(c x))^2/(d + i c d x)^2 and seven like it ran out of time.
https://github.com/asc-community/AngouriMath/issues/718

























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