Question

Integrate the following function with respect to $x$
$\frac{({\sin }^{-1}x{)}^{3/2}}{\sqrt{1-x^2}}$

Answer 1

According to question,

Let, $si{n}^{-1}x=t$

$⟹\frac{1}{\sqrt{1-x^2}}dx=dt$

Substituting these values, we get

$⟹\int t^{\frac{3}{2}}dt$

$⟹\frac{2t^{\frac{5}{2}}}{5}+C$

$⟹\frac{2(si{n}^{-1}x{)}^{\frac{5}{2}}}{5}+C$