Show that $\frac{B(x,y)}{c^{y}} = \int_{0}^{\infty} \frac{t^{x-1}}{{(c+t)}^{x+y}}$
45725
Derivation of an identity with beta function.
24716
$\int_0^\infty\frac{\log x dx}{x^2-1}$ with a hint.
6619
Prove that $\lim \limits_{(x,y,z) \to (0,0,0)} \frac{{xyz}}{{x+y+z}}=0$
36366
Prove $\int_0^\infty \frac{\sin^4x}{x^4}dx = \frac{\pi}{3}$
104853
Proving that $\lim\limits_{n\to\infty}n\left( \int_0^1 f(t)\, dt -\frac1n\sum_{k=0}^{n-1}f\left(\frac k n\right) \right)=\frac{f(1)-f(0)}{2}$
89602
$ \int_{0}^{ \infty} \int_{0}^{ \infty} \frac { e^{-(x+y)}}{x+y} dx dy $
69978
Evaluating $\int_1^\infty \frac{1}{x(x^2+1)}\ dx$
84034
Evaluate $\int_{-\infty}^{\infty} \chi_{[0,1]}(x-y) \chi_{[0,1]}(y) \, \mathrm{d}y$
82612
Show that $\frac c {1+c} \le \frac a {1+a} + \frac b {1+b}$ , for $c \le a+b$ and $a,b,c \ge 0$
84765
Evaluating $\int_{-\infty}^{\infty}\frac{1}{(x^2+b^2)^2}dx$
63251
Evaluation of $\int^1_0\frac{x^b-x^a}{\ln x} d x=\ln{{\frac{1+b}{1+a}}}$
139057
Showing that $\frac{1}{2\pi}\int^{2\pi}_{0}(2\cos\theta)^{2n}d\theta=\frac{(2n)!}{n!n!}$
23522
Exponential integral $ \int_0^\infty \frac{x^t}{\Gamma(t+1)}\text dt$
143375
Showing that $\lim_{(x,y) \to (0, 0)}\frac{xy^2}{x^2+y^2} = 0$
83703
Show that $\int_{0}^{\infty}|\frac{\sin x}{x}|\,dx=\infty $
24558
Show that $\frac{1}{\sqrt{2\pi}} \cdot \left(\int_{- \infty}^{\infty} e^{itx} \cdot e^{-\frac{1}{2}t^2 } dx \right) = e^{-\frac{1}{2}t^2}$
54266
Prove that $\int_a^b \left( \int_c^d f(x,y)dy\right) dx=\int_c^d \left( \int_a^b f(x,y)dx\right) dy$