New posts in Definite Integrals

Evaluate $\int_0^\infty \frac{(\mathrm{e}^{-ax}-\mathrm{e}^{-bx})^2}{x^2}dx=\ln\frac{(2a)^{2a}(2b)^{2b}}{(a+b)^{2(a+b)}} $

$\underset{x\to 1}{\text{lim}}\int_0^x \frac{\sqrt{t} f(t)}{\sqrt{f(x)-f(t)}} \, \mathrm dt=\frac{ \pi }{\sqrt{2}}$

What is the sign of the integral $\int_{0}^{2\pi}e^{\sin(x)}\cos(nx)\,dx$?

How to compute $\int_0^\infty \frac{\tanh\left(\pi x\right)}{x\left(1+x^2\right)} \, \mathrm{d}x$?

Express an integral in terms of another integral.

A problem related to $2x^3-3x^2-x+\frac{3}{2}=0$

Proof Verification of $|\cos(a) - \cos(b)| \leq |b-a|$

Integration by parts for definite integrals

Asymptotic behavior of a Fourier/Laplace transform

Evaluating the challenging sum $\sum _{k=1}^{\infty }\frac{H_{2k}}{k^3\:4^k}\binom{2k}{k}$.