posted by Sarah
∫ tan^2 x sec^3 x dx
If the power of the secant n is odd, and the power of the tangent m is even, then the tangent is expressed as the secant using the identity
1 + tan^2 x = sec^2 x
I thought that since tan is even and sec is odd, we have to put this in terms of cosine and sine.
= ∫ (sin^2 x / cos^2 x) (1/ cos^3 x) dx
= ∫ sin^2 x / cos^5 x dx
u = sin x
du= cos dx
= ∫ sin^2 x cos^-5 x dx
=∫ u^2 cos^-5 x (du/cos x)
= ∫ u^2 / (1 - u^2)^3 du
then split this into two integrals, but how do you do this? Thank you
please for any help. I'm just really confused with this problem.