Newbetuts

if $\int_1^{\infty}f(x)\ \mathrm dx$ converges, must $\int_1^{\infty}f(x)\sin x\ \mathrm dx$ converge?

If a function $ f $ is continuously differentiable and $ \int_0^{\infty} f(x)dx$ converges then $ f $ is bounded.

Prove that $\int_0^\infty \frac{e^{\cos(ax)}\cos\left(\sin (ax)+bx\right)}{c^2+x^2}dx =\frac{\pi}{2c}\exp\left(e^{-ac}-bc\right)$

How to find $\mathrm{\sum_{n=1}^\infty E_{n}(n)= \lim_{k\to\infty}\int_1^\infty \frac{e^{kt+t}t^k-e^t}{e^{kt+2t}t^{k+1}-e^{kt+t}t^k}dt=.26929…}$?

Proving the divergence of a infinite integral

Show $\int_0^\infty \frac{\ln^2x}{(x+1)^2+1} \, dx=\frac{5\pi^3}{64}+\frac\pi{16}\ln^22$

Unusual integral

Evaluating $\int_0^\infty \frac{\cos(ax)-e^{-ax}}{x \left(x^4+b^4 \right)}dx$

Calculate $\int_{-\infty}^{+\infty}\frac{x}{1+x^2}dx$, what is wrong with this?

$\int_{-\infty}^\infty \frac{\sin (t) \, dt}{t^4+1}$ must be zero and it isn't

Hints on calculating the integral $\int_0^1\frac{x^{19}-1}{\ln x}\,dx$

How to calculate this improper integral?

Compute $\int_{-\infty}^{+\infty}(1+\frac{1}{v^2})\exp(-\frac{u^2}{2\sigma_1^2\sigma_2^2}(\sigma_2v+\frac{\sigma_1}{v})^2)\,dv$

Integral of $\ln(x)\operatorname{sech}(x)$

Evaluate $\int_{0}^{\infty} \frac{{(1+x)}^{-n}}{\log^2 x+\pi^2} \ dx, \space n\ge1$

New posts in improper-integrals

Evaluating $\int_0^1 \frac{1}{\sqrt{\Gamma(x)}} dx$

does $\intop_{1}^{\infty}x\sin(x^{3})dx$ really converge?

Multiplying two integrals becomes a double integral?

How to find closed-form of $\int_{0}^{+\infty} \operatorname{sech}^2 (x^2)\,dx$

The integral : $\frac{1}{2}\int_0^\infty x^n \operatorname{sech}(x)\mathrm dx$

if $\int_1^{\infty}f(x)\ \mathrm dx$ converges, must $\int_1^{\infty}f(x)\sin x\ \mathrm dx$ converge?

If a function $ f $ is continuously differentiable and $ \int_0^{\infty} f(x)dx$ converges then $ f $ is bounded.

Prove that $\int_0^\infty \frac{e^{\cos(ax)}\cos\left(\sin (ax)+bx\right)}{c^2+x^2}dx =\frac{\pi}{2c}\exp\left(e^{-ac}-bc\right)$

How to find $\mathrm{\sum_{n=1}^\infty E_{n}(n)= \lim_{k\to\infty}\int_1^\infty \frac{e^{kt+t}t^k-e^t}{e^{kt+2t}t^{k+1}-e^{kt+t}t^k}dt=.26929…}$?

Proving the divergence of a infinite integral

Show $\int_0^\infty \frac{\ln^2x}{(x+1)^2+1} \, dx=\frac{5\pi^3}{64}+\frac\pi{16}\ln^22$

Unusual integral

Evaluating $\int_0^\infty \frac{\cos(ax)-e^{-ax}}{x \left(x^4+b^4 \right)}dx$

Calculate $\int_{-\infty}^{+\infty}\frac{x}{1+x^2}dx$, what is wrong with this?

$\int_{-\infty}^\infty \frac{\sin (t) \, dt}{t^4+1}$ must be zero and it isn't

Hints on calculating the integral $\int_0^1\frac{x^{19}-1}{\ln x}\,dx$

How to calculate this improper integral?

Compute $\int_{-\infty}^{+\infty}(1+\frac{1}{v^2})\exp(-\frac{u^2}{2\sigma_1^2\sigma_2^2}(\sigma_2v+\frac{\sigma_1}{v})^2)\,dv$

Integral of $\ln(x)\operatorname{sech}(x)$

Evaluate $\int_{0}^{\infty} \frac{{(1+x)}^{-n}}{\log^2 x+\pi^2} \ dx, \space n\ge1$