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