AngouriMath
SolveByWritingAPowerOfTheSecantInTheCosine(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
A half-odd power of the secant or the cosecant, in an integrand with the cosine or the
sine of the same argument in it, written as a power of the cosine or the sine:
sec(z)^p = K/cos(z)^p with K = sec(z)^p cos(z)^p , which is 1 wherever the
cosine is positive and -1 wherever it is negative, so it stands in front of the answer.
sine of the same argument in it, written as a power of the cosine or the sine:
cosine is positive and -1 wherever it is negative, so it stands in front of the answer.
Remarks
was answered: the substitutions that read a function of the cosine read the secant as
secant with no cosine keeps the rules for the secant. Rubi's 4.2.2.1, 4.2.3.1 and
4.2.4.2.
the integrand is then real exactly where the rewritten one is, and an answer for the
rewritten one, which holds where it is real, holds where the integrand is. A constant
inside the power,
side, and the integrand real where the rewritten one is not: for a negative
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