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Let F(x) = f(x) + f(1/x), where f(x) = ∫₁^x (log t)/(1 + t) dt. Then F(e) equals

1. 1
2. 2
3. 1/2
4. 0

Correct answer: 1/2

Solution

To find F(e), we evaluate f(e) and f(1/e). The integral f(x) is symmetric around x=1, leading to the result that f(e) + f(1/e) equals 1/2, thus making F(e) equal to 1/2.

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