New posts in Improper Integrals

How to calculate $\int _{-\infty }^{\infty }\frac{x\sin \left(x\right)}{1+x^4}\,dx$

$\int_ {0}^{\infty} \frac{(e^{3x}-e^x)dx}{x(e^x+1)(e^{3x}+1)}$

Calculate: $\int_0^\infty [x]e^{-x} \, dx$ where $[x]:=\max \{k\in\mathbb{Z}:k\leq x\}$

How to evaluate $\int _0^1\frac{\ln ^2\left(1-x\right)\ln ^3\left(1+x\right)}{1+x}\:dx$

Prove $\int_0^{\infty} \frac{\arctan{(x)}}{x} \ln{\left(\frac{1+x^2}{{(1-x)}^2}\right)} \; \mathrm{d}x = \frac{3\pi^3}{16}$

Evaluating $\int _0^1\frac{\ln \left(x^3+1\right)}{x+1}\:dx$

What is value of this integral? $\int_{0}^{\infty}\frac{\log(1+4x^2)(1+9x^2)(9+x^2)+(9+x^2)\log(4+x^2)(10+10x^2)}{(9+x^2)^{2}(1+9x^{2})}dx$

Challenging problem: Find $a$ where $\int_0^\infty \frac{\cos(ax)\ln(1+x^2)}{\sqrt{1+x^2}}dx=0$.

Find for which $\alpha$ the integral $\int_{0}^{1} \frac{1-x^{\alpha}}{1-x}dx$ converges

Evaluate $\int_0^{\infty} x^2\ln(\sinh x)\operatorname{sech}(3 x){\rm d}x $.