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Evaluate the integral ∫_0^1 [ln(1+x)/x] dx.
Hard
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Get StartedEvaluate the integral ∫_0^1 [ln(1+x)/x] dx.
Options:
- π^2/12
- π^2/6
- (ln 2)^2/2
- π^2/8
Correct answer: π^2/12
Explanation: Expand ln(1+x)=∑_{n≥1} (−1)^{n+1} x^n/n and integrate termwise to get ∑_{n≥1} (−1)^{n+1}/n^2 = π^2/12. The concrete value is π^2/12 ≈ 0.82217.
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