Evaluate $\int ( 3x + \frac{6x^2 \sin^2(\frac{x}{2})}{x - \sin x} ) \frac{(x-\sin x)^{3/2}}{\sqrt{x}} \mathrm{d}x$ I have a really vague integration problem. It's some substitution and then integration by parts maybe. 
I got this from a friend, but it seems it's unlikely​ to be solved.

 Now my question is, how to approach such big problems?
I reduced it to $$\displaystyle{\int \bigg(3x(2x-x\cos x - \sin x)\sqrt{1-\frac{\sin x}{x}}} \bigg)\mathrm{d}x$$
How to proceed from here?


Easier way to solve this problem  
