New posts in Improper Integrals

Evaluating $\int _0^1\frac{\ln \left(x^2+x+1\right)}{x\left(x+1\right)}\:dx$

How to prove convergence of the integral $\int_{0}^{\infty} x^{-a}\sin(x)dx$ for all $0<a<2$.

Integrate $\int_{-\infty}^{\infty} \frac{e^{2020x}-e^{x}}{x\left(e^{2020x}+1\right)\left(e^x+1\right)} \mathop{dx}$

Evaluate $\int_0^1 \ln{\left(\Gamma(x)\right)}\cos^2{(\pi x)} \; {\mathrm{d}x}$

Can we represent an improper integral as $\int_{-\infty}^{\infty} f(x)\,dx = \lim_{a \to \infty} \int_{-a}^a f(x)\,dx$?

Closed form of $\int_0^\infty \arctan^2 \left (\frac{2x}{1 + x^2} \right ) \, dx$

Is $\int_E \frac{1}{(x^2+y^2)^2}dxdy$ convergent?

Find $\int_{0}^{\infty} \frac{\log(x) }{\sqrt{x} (x+1)^{2}}\,dx$

Evaluate a real integral, e.g. $\int_{0}^{\infty}\frac{x^2}{(x^2+1)(x^2+4)}\:\mathrm dx$ with complex analysis

How to compute $\int_0^{\frac{\pi}{2}}\frac{\arctan(\sqrt{\tan(x)})}{\tan(x)}dx$