How Do You Integrate tan^2(x) * sec^3(x) dx?

[recon_ind]

Homework Statement

[PLAIN]http://integrals.wolfram.com/images/integral.gif(tan[x]^2*sec[x]^3)dx[/URL]

Homework Equations

Whatever you need to complete problem

The Attempt at a Solution

This problem has given me so much grief. I have page loads of work but can't figure it out.

 

[tiny-tim]

Welcome to PF!

Hi recon_ind! Welcome to PF!

tan²x sec³x = sec⁵x - sec³x …

so start with ∫sec³x dx …

use integration by parts (sec²x secx), and fiddle around with it.

Then that should give you an idea for sec⁵x