AngouriMath
SolveAnOddPowerOfTheTangentBesideAFunctionOfTheSecant(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
An odd whole power of tan(y) beside a function of sec(y) , integrated in
u = sec(y) : du = sec(y) tan(y) dy and the even power of the tangent left over
is a power ofu^2 - 1 , so tan(y)^n with the rest is
(u^2 - 1)^((n - 1)/2)/u du beside it, exactly. The cotangent beside a function of
the cosecant, inu = csc(y) , the same.
is a power of
the cosecant, in
Remarks
Rubi's cot(c + d x)/(a + b sec(c + d x))^(3/2) was declined and
cot(c + d x)^3 sqrt(a + b sec(c + d x)) ran past thirty seconds, where in the
secant each is a rational function beside the root of a linear. A power free of
x is read whatever its exponent: Rubi's (b sec(e + f x))^m tan(e + f x)^3 ,
4.3.0, was declined only becausem was not a number, where in u it is
(b u)^m (u^2 - 1)/u .
https://github.com/asc-community/AngouriMath/issues/718
https://github.com/asc-community/AngouriMath/issues/233
secant each is a rational function beside the root of a linear. A power free of
4.3.0, was declined only because
https://github.com/asc-community/AngouriMath/issues/718
https://github.com/asc-community/AngouriMath/issues/233
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