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Evaluate: (i) intxtan^(-1)x\ dx...

Evaluate: (i) `intxtan^(-1)x\ dx`

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To evaluate the integral \( I = \int x \tan^{-1}(x) \, dx \), we will use the method of integration by parts. ### Step 1: Identify \( u \) and \( dv \) We choose: - \( u = \tan^{-1}(x) \) (the inverse trigonometric function) - \( dv = x \, dx \) (the algebraic function) ### Step 2: Differentiate \( u \) and Integrate \( dv \) ...
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