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Evaluate: inttan^(-1)((2x)/(1-x^2))\ dx...

Evaluate: `inttan^(-1)((2x)/(1-x^2))\ dx`

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To evaluate the integral \( I = \int \tan^{-1}\left(\frac{2x}{1 - x^2}\right) \, dx \), we will use a substitution method and integration by parts. Here’s a step-by-step solution: ### Step 1: Substitution Let \( x = \tan \theta \). Then, we have: \[ dx = \sec^2 \theta \, d\theta \] ...
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