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The value of the integral \({\int }_{0}^{\infty }\frac{{\log }_{e}(x)}{{x}^{2}+4}dx\) is: [JEE Main 2026, 5 Apr (Shift 1…

Q1

The value of the integral \({\int }_{0}^{\infty }\frac{{\log }_{e}(x)}{{x}^{2}+4}dx\) is:

[JEE Main 2026, 5 Apr (Shift 1)]

a

\(\frac{\pi {\log }_{e}(2)}{2}\)

b

\(\frac{\pi {\log }_{e}(2)}{4}\)

c

\(1+\pi {\log }_{e}(2)\)

d

\(2+\pi {\log }_{e}(2)\)

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