i gave it a shot and this is what i got
= (1/cosx)(1/cosx)(sinx/cosx) (I REWROTE IT)
= (secx)(secxtanx) (TIME TO INTEGRATE)
= (secxtanx)(secx) + C
did i do it right?
No, I think I would approach it with the substitution:
$\displaystyle u=\cos(x)\,\therefore\,du=-\sin(x)\,dx$ and we have:
$\displaystyle -\int u^{-3}\,du=\frac{1}{2u^2}+C=\frac{1}{2\cos^2(x)}+C$
Using your approach, we could let:
$\displaystyle u=\sec(x)\,\therefore\,du=\sec(x)\tan(x)\,dx$ and we have the easier to integrate:
$\displaystyle \int u\,du=\frac{u^2}{2}+C=\frac{\sec^2(x)}{2}+C$
The two results are equivalent.