\hspace{-16}\bf{\int\frac{x^2.\cos^{-1}\big(x\sqrt{x}\big)}{\big(1-x^3\big)^2}dx}
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262I = \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
1or else the question converts to,
-13∫sin-1tt4 where t = √1-x3 which again is by-parts
