calculus II

∫ 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

asked by Sarah
  1. please for any help. I'm just really confused with this problem.

    posted by Sarah

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