Indefinite Integral $\int\frac{ \sin^3 2x-x \cos^3 x}{\cos^2 x}~dx $ How can I calculate $\displaystyle \int\frac{ \sin^3 2x-x \cos^3 x}{\cos^2 x} dx$? Help me I'm quite blur and  how should I start. A little show on working are gladly appreciated.

Hint:
Expand and arrive at (which should prove easier)
$$ \int 8 \sin^3(x) \cos(x)~dx-\int x \cos(x) ~dx$$
