Evaluate the improper integral $\int_{0}^{\infty}{f(x)-f(2x)\over x}dx$, where $\lim_{x \to \infty} f(x) = L$
717
Proof of Frullani's theorem
98710
Finding $\int_0^{\infty}xe^{-\lambda x} \, dx$
90095
Integrate $\int_0^{\infty } \frac{\cos x}{x} dx$
151149
$\lim_{n \to \infty} n \int_{1}^{\infty} \frac{dx}{1+x^n}$, solution critique needed
21375
The integral $\int_0^\infty \dfrac{x \sin(x)}{x^2+1} dx$
155981
Evaluate an proper integral:$\int_0^\infty x\left(\log\left(\frac1{x^2}\right)\right)^n dx$
87273
Evaluate the integral $\int_0^{\infty} \lfloor x \rfloor e^{-x}\mathrm dx$
83703
Show that $\int_{0}^{\infty}|\frac{\sin x}{x}|\,dx=\infty $
67837
Evaluation of $\int_{0}^{1}\frac{x\ln (x)}{\sqrt{1-x^2}}dx$
114195
Evaluating $\int_0^\infty \frac{\log (1+x)}{1+x^2}dx$
84034
Evaluate $\int_{-\infty}^{\infty} \chi_{[0,1]}(x-y) \chi_{[0,1]}(y) \, \mathrm{d}y$
19526
Integral of an integral with variable limits
40881
Evaluate $\int_{0}^{+\infty }{\left( \frac{x}{{{\text{e}}^{x}}-{{\text{e}}^{-x}}}-\frac{1}{2} \right)\frac{1}{{{x}^{2}}}\text{d}x}$
17454
Evaluate the integral $\int_0^n \frac{f(x)}{f(x) + f(n-x)}dx $
20404
Prove that $f$ continuous and $\int_a^\infty |f(x)|\;dx$ finite imply $\lim\limits_{ x \to \infty } f(x)=0$
85949
Integral involving logarithm: $\int_0^\infty \frac{ \ln x}{(x+a)(x+b)} dx$
116498
Convergence of improper integral $\int_{0}^{1}\frac{\log(x)}{1-x^2}dx$