Find the antiderivative of [tex]sin^4(x)tan^2(x)[/tex]
Trig identities I may have overlooked.
The Attempt at a Solution
I tried writing the integrand in terms of sin and cos but that didn't seem to lead anywhere. I tried integration by parts since the antiderivative of [tex]tan^2(x)[/tex] is [tex]tanx - x + C[/tex], but that approach lead to a more difficult integral that might have been solved using a messier integration by parts.
This isn't really homework since I'm in a theoretical calc course and we begin the theory of integration next quarter (in fact, we're on break). Anyways I used to be pretty good with elementary terms integration but I'm stuck. Could someone suggest a good first step? Thanks.