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

Explanation

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

### Step 1: Substitution
Let \( t = \sin^{-1} x \). Then, we have:
\[ x = \sin t \]
Differentiating both sides gives:
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