Question

Integration of x sine^-1 (X)/(1-X^2)1/2

Answer 1

do you mean \(\large \int \frac{x \ sin^{-1}x}{\sqrt{1-x^2}} \ dx\) ??

NB \((sin^{-1}x)^\prime = \frac{1}{\sqrt{1-x^2}}\), so IBP

try let \(u = sin^{-1}x, \ \ \ v' = \frac{x}{\sqrt{1-x^2}} \)