Newbetuts

How can we show that $\int_{-\infty}^{+\infty}{ke^x\pm1\over \pi^2+(e^x-x+1)^2}\cdot{(e^x+1)^2\over \pi^2+(e^x+x+1)^2}\cdot 2x \,\mathrm dx=k?$

Closed form of $I=\int_{0}^{\pi/2} \tan^{-1} \bigg( \frac{\cos(x)}{\sin(x) - 1 - \sqrt{2}} \bigg) \tan(x)\;dx$

Evaluating the integral $\int_{-1}^{1} \frac{\sqrt{1-x^{2}}}{1+x^{2}} \, dx$ using a dumbbell-shaped contour

Integrate $ \int_0^\infty \frac{ \ln^2(1+x)}{x^{3/2}} dx=8\pi \ln 2$

Tangent series representation

Integral $\int_0^{\pi/2} \theta^2 \log ^4(2\cos \theta) d\theta =\frac{33\pi^7}{4480}+\frac{3\pi}{2}\zeta^2(3)$

For which $L^p$ is $\pi=3.2$?

Does $\int_{0}^{\infty}{\cos(10x^2\pi)\sin(6x^2\pi)\over \sinh^2(2x\pi)}\mathrm dx={1\over 16}?$

Complex analysis - Finding $\int_0^\infty \frac{x\cos\left(\frac{1}{x^2}\right)}{x^4 + 4}\,dx$

Why is $\zeta(1+it) \neq 0$ equivalent to the prime number theorem?

Evaluate $\int_0^{\frac{\pi}{2}}\frac{x^2}{1+\cos^2 x}dx$

How do I evaluate this integral $\int_0^\pi{\frac{{{x^2}}}{{\sqrt 5-2\cos x}}}\operatorname d\!x$?

Using residues to evaluate a sum involving the square of $\text{csch}$

Integral $ \int_{-\infty}^{\infty}\frac{x^{2}}{\cosh\left(x\right)}\,{\rm d}x $

Asymptotic evaluation of $\int_0^{\pi/4}\cos(x t^2)\tan^2(t)dt$

New posts in contour-integration

Show that if $|\gamma_0(t) - y_1(t)| < |\gamma_0(t) - z|$, $w(\Gamma_0, z) = w(\Gamma_1, z)$

Integrating around a dog bone contour

Closed form of integral using contour integration

Contour integral $\oint_{|z|=1}\frac{z^2\sin(1/z)}{z-2}dz$

Computation integral with complex analysis

How can we show that $\int_{-\infty}^{+\infty}{ke^x\pm1\over \pi^2+(e^x-x+1)^2}\cdot{(e^x+1)^2\over \pi^2+(e^x+x+1)^2}\cdot 2x \,\mathrm dx=k?$

Closed form of $I=\int_{0}^{\pi/2} \tan^{-1} \bigg( \frac{\cos(x)}{\sin(x) - 1 - \sqrt{2}} \bigg) \tan(x)\;dx$

Evaluating the integral $\int_{-1}^{1} \frac{\sqrt{1-x^{2}}}{1+x^{2}} \, dx$ using a dumbbell-shaped contour

Integrate $ \int_0^\infty \frac{ \ln^2(1+x)}{x^{3/2}} dx=8\pi \ln 2$

Tangent series representation

Integral $\int_0^{\pi/2} \theta^2 \log ^4(2\cos \theta) d\theta =\frac{33\pi^7}{4480}+\frac{3\pi}{2}\zeta^2(3)$

For which $L^p$ is $\pi=3.2$?

Does $\int_{0}^{\infty}{\cos(10x^2\pi)\sin(6x^2\pi)\over \sinh^2(2x\pi)}\mathrm dx={1\over 16}?$

Complex analysis - Finding $\int_0^\infty \frac{x\cos\left(\frac{1}{x^2}\right)}{x^4 + 4}\,dx$

Why is $\zeta(1+it) \neq 0$ equivalent to the prime number theorem?

Evaluate $\int_0^{\frac{\pi}{2}}\frac{x^2}{1+\cos^2 x}dx$

How do I evaluate this integral $\int_0^\pi{\frac{{{x^2}}}{{\sqrt 5-2\cos x}}}\operatorname d\!x$?

Using residues to evaluate a sum involving the square of $\text{csch}$

Integral $ \int_{-\infty}^{\infty}\frac{x^{2}}{\cosh\left(x\right)}\,{\rm d}x $

Asymptotic evaluation of $\int_0^{\pi/4}\cos(x t^2)\tan^2(t)dt$