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Integrate the function (xcos^(-1)x)/(sqr...

Integrate the function `(xcos^(-1)x)/(sqrt(1-x^2))`

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To solve the integral \( \int \frac{x \cos^{-1} x}{\sqrt{1 - x^2}} \, dx \), we will use substitution and integration by parts. Here are the steps: ### Step 1: Substitution Let \( t = \cos^{-1} x \). Then, we differentiate both sides to find \( dx \): \[ x = \cos t \implies dx = -\sin t \, dt \] Also, we know that: ...
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