Ways to evaluate $\int_0^1 \int_0^1 \frac{1}{1-xy}dxdy = \frac{\pi^2}{6}$
29886
How to evaluate $\int_0^1\int_0^1 \frac{1}{1-xy} \, dy \, dx$ to prove $\sum_{n=1}^{\infty} \frac{1}{n^2}=\frac{\pi^2}{6}$.
104691
Integration of $\int_{0}^{1} \frac{x^k}{1-x} dx$
65982
Evaluate the improper integral $ \int_0^1 \frac{\ln(1+x)}{x}\,dx $
19475
Evaluate$\int_{-2}^2\int_{y^2-3}^{5-y^2}dxdy$
59667
Evaluating $\int_0^\infty\frac{\sin(x)}{x^2+1}\, dx$
153867
Evaluate $ \int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\:\mathrm dx$
115598
Evaluating $\int_{0}^{1} dx\frac{\log(1+x)}{1 + x^2}$
122361
Evaluate $\int_0^1\left(\frac{1}{\ln x} + \frac{1}{1-x}\right)^2 \mathrm dx$
74955
Simplify result of $\int_0^{\infty} \frac{1}{1+x^n}dx$
36586
Evaluating $\frac{1}{2\pi}\int_{0}^{2\pi}\frac{1}{1-2t\cos\theta +t^2}d\theta$
48233
Evaluating $\int_0^\infty \frac{dx}{1+x^4}$.
148613
Integrate $\int_{0}^{1}{x^{-x}(1-x)^{x-1}\sin{\pi x}dx}$
51488
Evaluating $\int^\pi_{-\pi} \cos^3(x) \cos(ax)~dx$
141892
How to evaluate $\int_0^\infty \frac{1}{x^n+1} dx$
7388
Evaluate: $\int_0^{\pi} \ln \left( \sin \theta \right) d\theta$
36701
$\displaystyle\int_{0}^{2\pi}\frac{1}{a+ \cos\theta}\,d\theta$
18732
How do I evaluate $\int \frac{\mathrm{d}x}{e^x + 1} $?