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

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

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To evaluate the integral \(\int \frac{x^2}{\sqrt{1-x^2}} \, dx\), we can use a trigonometric substitution. Here’s a step-by-step solution: ### Step 1: Substitution Let \(x = \sin \theta\). Then, we have: \[ dx = \cos \theta \, d\theta \] Also, we can express \(\sqrt{1 - x^2}\) as: ...
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