Integral of $\int \frac{\sin^22x}{\cos2x}\,\mathrm dx.$

Question

I would like to solve the following integral

$$\int \frac{\sin^22x}{\cos2x}\,\mathrm dx.$$ I know that the derivative of $\cos$ its $\sin$ but how its help me?
Any suggestions?
Thanks.

Answer 1

Hint:

$$\int \frac{\sin^2 2x}{\cos 2x}~dx ~ = ~ \int \sec 2x - \cos 2x~dx ~ = ~ \frac{1}{2} \int \sec u - \cos u ~ du \quad (u = 2x)$$