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

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

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To solve the integral \( I = \int \frac{x \sin^{-1} x}{\sqrt{1 - x^2}} \, dx \), we will use integration by parts and a substitution method. ### Step 1: Substitution Let \( t = \sin^{-1} x \). Then, we have: \[ x = \sin t \quad \text{and} \quad dx = \cos t \, dt \] Also, we know that: ...
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