Prove serial representation of the integral $\int_0^1 x^x \,{\rm d}x$
24508
Series as an integral (sophomore's dream)
45205
Showing that $\int_0^\infty x^{-x} \mathrm{d}x \leq 2$.
6552
Evaluation of the double integral $\int_{[0,1]×[0,1]} \max\{x, y\} dxdy$
78008
A conjectured closed form of $\int\limits_0^\infty\frac{x-1}{\sqrt{2^x-1}\ \ln\left(2^x-1\right)}dx$
76408
Show that $\int_0^\pi f(\sin x)\,\mathrm{d}x = 2\int_0^{\pi/2}f(\sin x) \, \mathrm{d}x$
126236
General closed form of $\int_{0}^{\theta_0} \frac{1}{\sqrt{\cos \theta-\cos \theta_0}} d\theta$
141926
A Challenging Logarithmic Integral $\int_0^1 \frac{\log(x)\log(1-x)\log^2(1+x)}{x}dx$
21240
Prove $\int_0^{\infty}\! \frac{\mathbb{d}x}{1+x^n}=\frac{\pi}{n \sin\frac{\pi}{n}}$ using real analysis techniques only
9518
Evaluate: $ \int_0^1 \int_y^1 e^{x^2 }dxdy$
1744
Quadruple Integral $\int\limits_0^1\!\!\int\limits_0^1\!\!\int\limits_0^1\!\!\int\limits_0^1\frac1{1-xyzw}\,dw\,dz\,dy\,dx$
9730
Solve the integral $\int_0^\infty x/(x^3+1) dx$
51284
$\int_{-\infty}^\infty \frac{e^{ax}}{1+e^x}dx$ with residue calculus
110343
Integrating $\rm x^ae^{-bx}$.
42805
Show that $\int\limits_0^1 \left(x^{x}\right)^{\left(x^{x}\right)^{\left(x^{x}\right)^{\left(x^{x}\right)^{⋰}}}}\ \mathrm{d}x=\frac{\pi^2}{12}$.
144039
Computing $ \int_0^{\infty} \frac{ \sqrt [3] {x+1}-\sqrt [3] {x}}{\sqrt{x}} \mathrm dx$
102636
Contour Integral: $\int^{\infty}_{0}(1+z^n)^{-1}dz$
82311
Computing the primitive $\int\frac{1}{1+x^n} dx$