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.

Let 
$$
  u = x^{2} \qquad \Rightarrow \qquad du = 2x dx
$$
Then the primitive becomes
$$
\int 4 x \sin \left(x^2\right) \cos \left(x^2\right) \, dx \Rightarrow
\int 2 \sin u \cos u \, du =
-\frac{1}{2} \cos (2 u) \, du  \Rightarrow
-\frac{1}{2} \cos \left(2 x^2\right)
$$
