Newbetuts

$\int_{-\infty}^{\infty}{e^x+1\over (e^x-x+1)^2+\pi^2}\mathrm dx=\int_{-\infty}^{\infty}{e^x+1\over (e^x+x+1)^2+\pi^2}\mathrm dx=1$

Does $\int_{0}^{\infty}{\sin{(\pi{x^2})}\over \sinh{(\pi{x}})\tanh(x\pi)}\mathrm{d}x$ have a simple closed from?

Is $\int_{\mathbb R} f(\sum_{k=1}^n\frac{1}{x-x_k})dx$ independent of $x_k$'s for certain $f$?

how to use Lebesgue dominated convergence theorem to evaluate the limit of a definite integral?

Evaluate $\int_{0}^{\large\frac{\pi}{4}} \ln {(\sin x)}\cdot\ln {(\cos x)} \left(\frac{\ln{(\sin x)}}{\cot x}+\frac{\ln {(\cos x)}}{\tan x}\right)dx$

Elementary Proof of Ramanujan Master Theorem

I want to show that $\int_{-\infty}^{\infty}{\left(x^2-x+\pi\over x^4-x^2+1\right)^2}dx=\pi+\pi^2+\pi^3$

Line integral with respect to arc length

Seeking Methods to solve $\int_{0}^{\infty} \frac{e^{-x^n}}{x^n + 1}\:dx $

LogSine Integral $\int_0^{\pi/3}\ln^n\big(2\sin\frac{\theta}{2}\big)\mathrm d\theta$

Find the closed form for $\int_{0}^{\infty}\cos{x}\ln\left({1+e^{-x}\over 1-e^{-x}}\right)dx=\sum_{n=0}^{\infty}{1\over n^2+(n+1)^2}$

Evaluating $\int_a^b \arccos\left(x\,/\sqrt{(a+b)x-ab\,}\,\right)\,\mathrm {d}x$ assuming $0<a<b$

Help me to finish calculating $\int_0^{\infty} \frac{1}{x^3-1}dx$

Evaluate: $I=\int\limits_{0}^{\frac{\pi}{2}}\ln\frac{(1+\sin x)^{1+\cos x}}{1+\cos x}dx$

Find $\int_0^1 \frac{f(x)}{\sqrt{1+x^2}}dx$

Evaluating $\int_{0}^{\infty} \left[\left(\frac{2015}{2015+x}+\cdots +\frac{2}{2+x}+\frac{1}{1+x}-x\right)^{2016}+1 \right] ^{-1}\mathrm{d}x$

Evaluation of $\int_0^1 \frac{x^3}{2(2-x^2)(1+x^2) + 3\sqrt{(2-x^2)(1+x^2)}}\,\mathrm dx$

New posts in definite-integrals

$\int_{-\infty}^{\infty}{e^x+1\over (e^x-x+1)^2+\pi^2}\mathrm dx=\int_{-\infty}^{\infty}{e^x+1\over (e^x+x+1)^2+\pi^2}\mathrm dx=1$

Integral $\int_0^1 \frac{(x^2+1)\ln(1+x)}{x^4-x^2+1}dx$

Integral $\int_0^\infty\Big[\log\left(1+x^2\right)-\psi\left(1+x^2\right)\Big]dx$

Closed form of $\int_0^{\pi/2} \frac{\arctan^2 (\sin^2 \theta)}{\sin^2 \theta}\,d\theta$

Does $\int_{0}^{\infty}{\sin{(\pi{x^2})}\over \sinh{(\pi{x}})\tanh(x\pi)}\mathrm{d}x$ have a simple closed from?

Is $\int_{\mathbb R} f(\sum_{k=1}^n\frac{1}{x-x_k})dx$ independent of $x_k$'s for certain $f$?

how to use Lebesgue dominated convergence theorem to evaluate the limit of a definite integral?

Evaluate $\int_{0}^{\large\frac{\pi}{4}} \ln {(\sin x)}\cdot\ln {(\cos x)} \left(\frac{\ln{(\sin x)}}{\cot x}+\frac{\ln {(\cos x)}}{\tan x}\right)dx$

Elementary Proof of Ramanujan Master Theorem

I want to show that $\int_{-\infty}^{\infty}{\left(x^2-x+\pi\over x^4-x^2+1\right)^2}dx=\pi+\pi^2+\pi^3$

Line integral with respect to arc length

Seeking Methods to solve $\int_{0}^{\infty} \frac{e^{-x^n}}{x^n + 1}\:dx $

LogSine Integral $\int_0^{\pi/3}\ln^n\big(2\sin\frac{\theta}{2}\big)\mathrm d\theta$

Find the closed form for $\int_{0}^{\infty}\cos{x}\ln\left({1+e^{-x}\over 1-e^{-x}}\right)dx=\sum_{n=0}^{\infty}{1\over n^2+(n+1)^2}$

Evaluating $\int_a^b \arccos\left(x\,/\sqrt{(a+b)x-ab\,}\,\right)\,\mathrm {d}x$ assuming $0<a<b$

Help me to finish calculating $\int_0^{\infty} \frac{1}{x^3-1}dx$

Evaluate: $I=\int\limits_{0}^{\frac{\pi}{2}}\ln\frac{(1+\sin x)^{1+\cos x}}{1+\cos x}dx$

Find $\int_0^1 \frac{f(x)}{\sqrt{1+x^2}}dx$

Evaluating $\int_{0}^{\infty} \left[\left(\frac{2015}{2015+x}+\cdots +\frac{2}{2+x}+\frac{1}{1+x}-x\right)^{2016}+1 \right] ^{-1}\mathrm{d}x$

Evaluation of $\int_0^1 \frac{x^3}{2(2-x^2)(1+x^2) + 3\sqrt{(2-x^2)(1+x^2)}}\,\mathrm dx$