AngouriMath
SolveAnOddPowerOfASineOverAPowerOfABinomialInTheSquaredTangentUnderTheCosine(AngouriMath.Entity,AngouriMath.Entity.Variable)
Method (no overloads)
Summary
An odd power of a sine over a whole power of a + b tan(y)^2 , under
u = cos(y) : a + b tan(y)^2 = ((a - b) u^2 + b)/u^2 and
sin(y)^m dy = -(1 - u^2)^((m - 1)/2) du , so the integrand is the rational
function-(1 - u^2)^((m - 1)/2) u^(2 n)/((a - b) u^2 + b)^n , asked with
a - b named by a symbol of its own and written back into the answer.
function
Remarks
Bioche's substitution, which comes after the substitution search: the search ran out
of time on Rubi's 4.3.7sin(e + f x)^3/(a + b tan(e + f x)^2)^3 , and took
fifteen seconds onsin^5/(a + b tan^2)^3 . The rational function with
a - b written in it took seven seconds, where named it takes a tenth of one.
The quadratic has no linear term, so the name hides no relation between its
coefficients;a = b is another shape, and declines.
https://github.com/asc-community/AngouriMath/issues/233
of time on Rubi's 4.3.7
fifteen seconds on
The quadratic has no linear term, so the name hides no relation between its
coefficients;
https://github.com/asc-community/AngouriMath/issues/233
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