Question

\[\int\frac{\left( \sin^{- 1} x \right)^3}{\sqrt{1 - x^2}} dx\]

 

Answer 1

\[\int\frac{\left( \sin^{- 1} x \right)^3}{\sqrt{1 - x^2}} dx\]
\[\text{Let }\sin^{- 1} x = t\]
\[ \Rightarrow \frac{1}{\sqrt{1 - x^2}}dx = dt\]
\[Now, \int\frac{\left( \sin^{- 1} x \right)^3}{\sqrt{1 - x^2}} dx \]
\[ = \int t^3 dt\]
\[ = \frac{t^4}{4} + C\]
\[ = \frac{\left( \sin^{- 1} x \right)^4}{4} + C\]