AngouriMath
SolveAnOddPowerOfATangentBesideAFunctionOfTheSquaredSineUnderIt(AngouriMath.Entity,AngouriMath.Entity.Variable)
Method (no overloads)
Summary
An odd power of a tangent beside a function of the square of the sine of the same
linear,tan(y)^(2 k + 1) F(sin(y)^2) , under v = sin(y)^2 : with
dv = 2 sin(y) cos(y) dy , tan(y)^(2 k + 1) dy = v^k/(1 - v)^(k + 1) dv/2 ,
andv^k F(v)/(2 (1 - v)^(k + 1)) is asked of the rest of the integrator.
linear,
and
Remarks
The substitution in the secant after it writes a + b sin(y)^2 as
a + b (1 - 1/u^2) , and writing the power of that quotient apart took eight
seconds on Rubi's 4.1.7tan(e + f x)^5/(a + b sin(e + f x)^2)^(5/2) , which
ran out of time; inv it is a power of a linear beside a rational function,
answered in a tenth of a second. Only where a root holds the sine's square: a
rational function of it the secant's substitution answers as shortly.
https://github.com/asc-community/AngouriMath/issues/233
seconds on Rubi's 4.1.7
ran out of time; in
answered in a tenth of a second. Only where a root holds the sine's square: a
rational function of it the secant's substitution answers as shortly.
https://github.com/asc-community/AngouriMath/issues/233
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