Newbetuts

Proof $\int_0^\infty \frac{\exp(-\sqrt{x^2+y^2})}{x^2+y^2}dx = \frac{\pi}{2}\left(\frac{1}{y} - K_0(y)L_{-1}(y) - K_1(y)L_{0}(y)\right)$

Abel summability of integrals

Evaluate $\int_0^\infty \frac{dx}{(x+\sqrt{1+x^2})^2}$

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

Prove/Show that Limit is equal to 0.

Show that $\int^\infty_0\left(\frac{\ln(1+x)} x\right)^2dx$ converge.

$\int_{-\infty}^\infty f(x)dx$ vs. $\lim_{b\rightarrow\infty}\int_{-b}^b f(x)dx$ for odd $f(x)$.

How evaluate the following hard integrals?

Computing $\lim_{\epsilon \rightarrow 0} \int_0^\infty \frac{\sin x}{x} \arctan{\frac{x}{\epsilon}}dx$

Show that $\int_0^{\infty}\frac{f(ax)-f(bx)}{x}dx=[f(0)-L]\ln\frac{b}{a}$ [duplicate]

How to study the convergence of $ \int_{0}^{\infty}\frac{dx}{1+x^{2}|\sin(x)|} $?

Trans series for an integral

Why isn't an odd improper integral equal to zero

How to "fix" $\int_{-1}^1 \frac {dx}{x^2}$ with complex numbers?

Other integral related to Ahmed's integral

Convergence of $ I=\int_0^\infty \sin x\sin(x^2)\mathrm{d}x$

New posts in improper-integrals

Frullani integral $\int_0^\infty \frac{\text{csch}(x)-\frac1x}{x} {\rm d}x$

How to integrate $f(x) =\exp(-ax-b/x)$?

A complex approach to integral of cardinal sine [duplicate]

Evaluating $\int_{0}^{2\pi}x^2\ln^2(1-\cos x)dx$

Proof $\int_0^\infty \frac{\exp(-\sqrt{x^2+y^2})}{x^2+y^2}dx = \frac{\pi}{2}\left(\frac{1}{y} - K_0(y)L_{-1}(y) - K_1(y)L_{0}(y)\right)$

Abel summability of integrals

Evaluate $\int_0^\infty \frac{dx}{(x+\sqrt{1+x^2})^2}$

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

Prove/Show that Limit is equal to 0.

Show that $\int^\infty_0\left(\frac{\ln(1+x)} x\right)^2dx$ converge.

$\int_{-\infty}^\infty f(x)dx$ vs. $\lim_{b\rightarrow\infty}\int_{-b}^b f(x)dx$ for odd $f(x)$.

How evaluate the following hard integrals?

Computing $\lim_{\epsilon \rightarrow 0} \int_0^\infty \frac{\sin x}{x} \arctan{\frac{x}{\epsilon}}dx$

Show that $\int_0^{\infty}\frac{f(ax)-f(bx)}{x}dx=[f(0)-L]\ln\frac{b}{a}$ [duplicate]

How to study the convergence of $ \int_{0}^{\infty}\frac{dx}{1+x^{2}|\sin(x)|} $?

Trans series for an integral

Why isn't an odd improper integral equal to zero

How to "fix" $\int_{-1}^1 \frac {dx}{x^2}$ with complex numbers?

Other integral related to Ahmed's integral

Convergence of $ I=\int_0^\infty \sin x\sin(x^2)\mathrm{d}x$