MHB Inverse Integral: $\int \frac{x^2\cos^{-1}\left(x\sqrt{x}\right)}{(1-x^3)^2}dx$

[juantheron]

$\displaystyle \int \frac{x^2\cos^{-1}\left(x\sqrt{x}\right)}{(1-x^3)^2}dx$

 

[Amer]

integrate by parts dv = \frac{x^2}{(1-x^3)^2} and u = \cos ^{-1} (x \sqrt{x} )