AngouriMath
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OverTheFunctionLessARoot(AngouriMath.Entity,System.Boolean,AngouriMath.Entity,AngouriMath.Entity)
Method (no overloads)
Summary
int dx/(sin(k x + m) - r), or the same of the cosine, for any complex
root: -2 atan((r t - 1)/sqrt(r^2 - 1))/(k sqrt(r^2 - 1)) with t = tan((k x + m)/2), and -2 atan(t/σ)/(k (1 + r) σ) with
σ = sqrt((r - 1)/(r + 1)). Each differentiates back to the integrand for
every value of the root but ±1, the arctangent of an imaginary argument being
the hyperbolic one with a constant imaginary part a derivative does not see; at
±1 the integral is rational in t.
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