Dear adiman84,

what is the main problem in the ugly integral? The 3th root -- I think so.

Therefore substitute x = z^3. I hope you know the method of substitution in integral.

if you carry out it will appear (among other things) a term:

That suggest stong a new substitution: z = cos(w) or z = sin(w).

I hope you can do it in more detail and you can continue.