How do I find the indefinite integral of cosx/(1-cos^2 x)dx?

Answer 1

cosx/(1-cos^2 x)
= cosx/(sin^2 x)
= (cosx/sinx)(1/sinx)
= cotx cscx

I just happen to know, as should you, that the derivative of cscx = -cotx cscx

so ∫cosx/(1-cos^2 x) dx = - cscx