I need to find out if integral converges:
$$\displaystyle\int_{0}^{1} \frac{\mathrm dx}{\sqrt{(1-x)\ln(1+x)}}$$
Any suggestions? Thanks.
2026-05-15 08:01:35.1778832095
Does improper integral converge?
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At zero: $$\frac{1}{\sqrt{(1-x)\ln(1+x)}}\sim_0\frac{1}{\sqrt{x}}$$ so the given integral is convergent at $0$.
Moreover at $1$ we have $$\frac{1}{\sqrt{(1-x)\ln(1+x)}}\sim_0\frac{1}{(1-x)^{1/2}\sqrt{2}}$$ so the integral exists at $1$ and hence the integral converges.