Integral with inequality: $\int_a^\infty e^{-x^{2}}dx≤ \frac 1{2a}e^{-a^{2}} $
9938
Proof of upper-tail inequality for standard normal distribution
76400
Finding $\int^{\infty}_{0}\frac{\ln^2(x)}{(1-x^2)^2} dx$
68097
Prove $\int\limits_{0}^{\infty} \mathrm{exp}(-ax^{2}-\frac{b}{x^{2}}) \mathrm{d} x = \frac{1}{2}\sqrt{\frac{\pi}{a}}\mathrm{e}^{-2\sqrt{ab}}$
15569
Integral of the form $\int_0^\infty \exp{\left(-\frac{(a+bx)^2}{x}\right)}\frac{dx}{\sqrt{x^3}}$
156531
Evaluating the integral $\int_{-\infty}^\infty \frac{\sin^2(x)}{x^2}e^{i t x} dx$
158180
An inequality of $\int_0^1 |f(x)|dx$
136602
Why is $\int_1^{\infty}(1/x^2)\,dx$  less than $\sum_{n=1}^{\infty} 1/(n^2)$?
100180
Evaluate the integral $\int_0^\infty \frac{dx}{\sqrt{(x^3+a^3)(x^3+b^3)}}$
102932
Integral $\int_0^\infty \frac{\arctan(x) dx}{x(1+x^2)}$?
6014
Evaluating $\int_{-\infty}^{\infty}\frac{\exp\left(-a x^2\right)}{x^2+b^2}dx$
40537
How to prove $\int_0^\infty e^{-x^2}cos(2bx) dx = \frac{\sqrt{\pi}}{2} e^{-b^2}$
128790
Prove an integral inequality: $ \left(\int|f|^2dx\right)^2\le 4\left(\int|xf(x)|^2dx\right)\left(\int|f'|^2dx\right) $
81742
Integral inequality (Cauchy-Schwarz)
35861
Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$
93759
Evaluate $\int_{0}^{\infty} \frac{e^{ax}-e^{bx}}{(1+e^{ax})(1+e^{bx})} dx$
8934
How do I solve this improper integral: $\int_{-\infty}^\infty e^{-x^2-x}dx$?
79908
Show $\int_0^\infty \frac{e^{-x}-e^{-xt}}{x}dx = \ln(t),$ for $t \gt 0$