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

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

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To evaluate the integral \( I = \int \sin^{-1}\left(\frac{2x}{1+x^2}\right) \, dx \), we can follow these steps: ### Step 1: Simplify the Argument We start with the expression inside the inverse sine function: \[ \frac{2x}{1+x^2} \] This expression can be recognized as the sine of a double angle. Specifically, we can use the identity: ...
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