Teaching DSSSB TGT Mock Test 2025 Mathematical Science Analysis Improper Integrals

Which of the following improper integral is convergent?

1
\(\int_2^\infty \frac{1}{\log x}\) dx
2
\(\int_0^1 \frac{1}{\sqrt{x}(x + 1)}\) dx
3
\(\int_1^2 \frac{\sqrt{x}}{\log x}\) dx
4
\(\int_0^\pi \frac{1}{1 - \cos x}\) dx
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