AngouriMath
SolveAFunctionOfAnInverseTimesItsDerivativeUpToAConstant(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
A function of an inverse sine, cosine or tangent u of something not linear, times
u' up to a factor that is constant though written with x in it:
integral G(u) K u' dx = K integral G(t) dt at t = u .
atan(c x/sqrt(a - c^2 x^2)) has the derivative c/sqrt(a - c^2 x^2) , and beside it
1/sqrt(d - c^2 d x^2/a) is that over c times sqrt(a - c^2 x^2)/sqrt(d - c^2 d x^2/a) ,
which is constant wherever it is real.
which is constant wherever it is real.
Remarks
The factor is taken as constant only where its derivative is zero as a value. Rubi's 5.3.7
atan(c x/sqrt(a - c^2 x^2))^m/sqrt(d - c^2 d x^2/a) and the like were declined.
https://github.com/asc-community/AngouriMath/issues/718
https://github.com/asc-community/AngouriMath/issues/718
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