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Evaluate the definite integral ∫₀¹ (8log(1+x))/(1+x²) dx.

1. (π)/(8)log 2
2. (π)/(2)log 2
3. log 2
4. πlog 2

Correct answer: πlog 2

Solution

The integral evaluates to ( rac{ ext{numerical constant}}{1+x²}) which, when integrated, yields a result involving ( rac{ ext{constant}}{8}) and the logarithm of 2, ultimately leading to the correct answer of ( rac{ ext{constant}}{8}) multiplied by ( ext{constant}) from the integration process.

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