Show that $\int_0^{\infty}\frac{\ln x}{1+x^2}\hspace{1mm}dx=0$
35861
Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$
19514
$\int_0^{\infty } \frac{\log (x)}{e^x+1} \, dx = -\frac{1}{2} \log ^2(2)$ How to show?
146349
$\int_0^\infty \frac{\ln\left(1+x-\sqrt{2x}\right)}{1+x^2}\,dx$
141892
How to evaluate $\int_0^\infty \frac{1}{x^n+1} dx$
151149
$\lim_{n \to \infty} n \int_{1}^{\infty} \frac{dx}{1+x^n}$, solution critique needed
85949
Integral involving logarithm: $\int_0^\infty \frac{ \ln x}{(x+a)(x+b)} dx$
42758
How to find $ \int_0^\infty \dfrac x{1+e^x}\ dx$
45205
Showing that $\int_0^\infty x^{-x} \mathrm{d}x \leq 2$.
102649
Prove that $\int_0^1\frac{x\ln (1+x)}{1+x^2}dx=\frac{\pi^2}{96}+\frac{\ln^2 2}{8}$
79908
Show $\int_0^\infty \frac{e^{-x}-e^{-xt}}{x}dx = \ln(t),$ for $t \gt 0$
67622
Proving of Integral $\int_{0}^{\infty}\frac{e^{-bx}-e^{-ax}}{x}dx = \ln\left(\frac{a}{b}\right)$
63956
Evaluate $\int_0^{\infty}\frac{\ln x}{x^a(x+1)}dx$ where $0<a<1$
91333
How to find $\int_{0}^{1}\dfrac{\ln^2{x}\ln^2{(1-x)}}{2-x}dx$
57686
Finding $ \int^1_0 \frac{\ln(1+x)}{x}dx$
45622
Value of this definite integral $\int_{0}^{\infty} \frac{ \ln(x)}{x^2+2x+4} dx $
74955
Simplify result of $\int_0^{\infty} \frac{1}{1+x^n}dx$
102399
Computing $ \int_0^\infty \frac{\log x}{\exp x} \ dx $