Stuck on an integral $4x\sin (x^2)\cos (x^2)$ I'm trying to get my head around this integral but it just doesn't click $$4x\sin (x^2)\cos (x^2) $$
I have tried substitution but I am confusing myself!
Do I substitute $\cos (x^2)$ getting $du=- 2x\sin (x^2) $ but I'm not sure where to go from there.

$$\int 4x\sin (x^2)\cos (x^2) \,dx $$
$$= \int 2\sin (x^2) \cos(x^2) \, dx^2$$
$$=\int 2\sin (x^2) \,  d\sin(x^2) $$
$$= \sin^2(x^2) + C $$
