Indefinite integral(28 april)

I = \hspace{-16}\bf{\int\frac{x^2.\cos^{-1}\big(x\sqrt{x}\big)}{\big(1-x^3\big)^2}dx}

Let x^{3/2} = cos\theta

\frac{3}{2} x^{1/2}dx = -sin\theta d\theta

I = -\int \frac{\theta .sin2\theta }{3sin^{4}\theta }d\theta

which can be calculated using by parts

or else the question converts to,
-13∫sin^-1tt⁴ where t = √1-x³ which again is by-parts