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Determine the result of the integral ∫_(-π/2)^(π/2) (x² cos x)/(1 + e^x) dx.

1. (π²)/(4) - 2
2. (π²)/(4) + 2
3. π² - e^(π/2)
4. π² + e^(π/2)

Correct answer: (π²)/(4) - 2

Solution

The integral is evaluated by first expressing it as a sum of two integrals from 0 to π/2, then simplifying the expression to find the final result of π²/4 - 2.

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