New posts in Definite Integrals

How to integrate $\int_0^{\infty} \frac{x}{e^x+1} dx$

Evaluating $\int_{0}^{\pi} \frac{1}{\sqrt{u^2+2u\cos x +1}} \mathrm{d}x$

One definite integral problem

For what $a$ and $b$ are there explicit expressions for $I(a, b) =\int_0^1 \int_0^1 \dfrac{dx\,dy}{1-x^ay^b} $?

Is there a direct proof for $\int_0^{2\pi}\frac{r^2+r(\cos t-\sin t)}{1+2r\cos t+r^2}dt=2\pi$

Find the closed-form solution to a integral with the floor function

Show that $\int_0^a \frac{\sin x}{x} dx \leq 1+\log a$ for all $a \geq 1$

How to integrate $\int_0^1\frac{dx}{1+x+x^2+\cdots+x^n}$

Solve integral $\int^1_0 \frac{1-x^2}{{(1+x^2)}\sqrt{1+x^4}}dx$ using subsituition $\sqrt{1+x^4} = {(1+x^2)}\cos{\theta}$

A simple proof for Glasser: $\int_{-\infty}^{\infty} f(x-a/x) dx=\int_{-\infty}^{\infty} f(x) dx, a>0$