Find the indefinite integral for sec^3x*tanx using u substitution.

I've done pretty well solving u substitution problems up to this point, but this problem continues to stump me; there is something I am missing.

let u=tanx

du = sec^2x*dx

I figure that maybe I can "break apart" the sec^3x term into sec^2x*secx, giving me the following:

sec^2x*secx*u*dx

But du=sec^2dx so substituting gives secx*u*du

But I can't find the anti derivative of this