Find : `int(xsin^(-1)x)/(sqrt(1-x^2))dx`

Explanation

To solve the integral \( \int \frac{x \sin^{-1}(x)}{\sqrt{1-x^2}} \, dx \), we will use the method of integration by parts. Here’s a step-by-step solution:

### Step 1: Substitution
Let \( t = \sin^{-1}(x) \). Then, we differentiate both sides to find \( dx \):
\[ dt = \frac{dx}{\sqrt{1-x^2}} \implies dx = \sqrt{1-x^2} \, dt \]
Also, since \( x = \sin(t) \), we can substitute \( x \) in the integral.
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