check that $\int_0^{\pi/2}\frac{1}{\sqrt{1-k^2sin^2\theta}}d\theta$ is equivalent to $-\log\sqrt{1-k^2}$ for $k\to1$.
121988
Asymptotic expansion of the complete elliptic integral of the first kind
149341
Help me evaluate $\int_0^1 \frac{\log(x+1)}{1+x^2} dx$
23368
Does $\int_1^2\frac{\sin{x}}{\log{x}} \, dx$ converge?
30731
Integral ${\frac{1}{\pi^2}} \int_{0}^{\infty}\frac{{(\ln{x}})^2}{\sqrt{x}{(1-x)^2}} \mathrm d x$
139057
Showing that $\frac{1}{2\pi}\int^{2\pi}_{0}(2\cos\theta)^{2n}d\theta=\frac{(2n)!}{n!n!}$
141926
A Challenging Logarithmic Integral $\int_0^1 \frac{\log(x)\log(1-x)\log^2(1+x)}{x}dx$
19514
$\int_0^{\infty } \frac{\log (x)}{e^x+1} \, dx = -\frac{1}{2} \log ^2(2)$ How to show?
149866
Evaluating $\int_0^{2\pi} \frac {\cos(\theta)}{5-3\cos(\theta)} \, d\theta$ using residue theorem
96486
Double Integral $\int_0^\infty \int_0^\infty \frac{\log x \log y}{\sqrt {xy}}\cos(x+y)\,dx\,dy=(\gamma+2\log 2)\pi^2$
152648
Is the integral $\int_1^\infty\frac{x^{-a} - x^{-b}}{\log(x)}\,dx$ convergent?
24974
Closed form for $\int_0^1\log\log\left(\frac{1}{x}+\sqrt{\frac{1}{x^2}-1}\right)\mathrm dx$
7388
Evaluate: $\int_0^{\pi} \ln \left( \sin \theta \right) d\theta$
96414
Using residues to evaluate the integral $\int_{-\pi}^{\pi} \frac{\cos(n\theta)}{1-2a\cos(\theta)+a^2}d\theta$, $|a|<1$
103598
Showing that $\int_0^1 \log(\sin \pi x)dx=-\log2$
81914
Integrating $\int_0^1 \frac {\log(1-x)\log^2(1+x)}x \mathrm{d}x$
1570
Show that log $Fib_{n}$ is $\theta(n)$
30459
Evaluate $\int^1_0 \log^2(1-x) \log^2(x) \, dx$