(TaNx) ^ 5 indefinite integral

(TaNx) ^ 5 indefinite integral

(TaNx) ^ 5 = (SiNx) ^ 5 / (COS x) ^ 5 let cos x = U
The original formula = - [(1-u ^ 2) ^ 2 / u ^ 5 Du] = (2 / u ^ 3 - 1 / u ^ 5 - 1 / U) Du = - u ^ - 2 + 1 / 4 * u ^ (- 4) + ln (U absolute value) + C can replace u with cosx