Newbetuts

Is it possible to evaluate the integral $I=\int_0^\infty \frac{\sqrt{x}\arctan(x)}{1+x^2}dx$ with residue theorem?

Evaluate $\int_0^{2\pi} \frac{\sin^2\theta}{5+4\cos\theta}\,\mathrm d\theta$

Evaluate some integrals with hypergeometric function

Closed form for $\int_0^\infty\frac{1}{(1+x^2)^s}\,dx$ when $s\in (0.5,\infty)\setminus\mathbb{N}$

Generalised Integral $I_n=\int_0^{\pi/2} \frac{x^n}{\sin ^n x} \ \mathrm{d}x, \quad n\in \mathbb{Z}^+.$

Alternative and more direct proof that an integral is independent of a parameter

Question about finite analog of $\int_0^\infty \frac{\sin x\sinh x}{\cos (2 x)+\cosh \left(2x \right)}\frac{dx}{x}=\frac{\pi}{8}$

Prove that a square-integrable entire function is identically zero

Mellin transform of $\sin x$ aka $\int^{\infty}_0 x^{s-1}\sin x dx $ [duplicate]

Is possible to use "Feynman's trick" (differentiate under the integral or Leibniz integral rule) to calculate $\int_0^1 \frac{\ln(1-x)}{x}dx\:?$

How to solve $\int_0^{\infty}\frac{\cos{ax}}{x^3+1}dx$?

closed form of $\int_{0}^{2\pi}\frac{dx}{(a^2\cos^2x+b^2\sin^2x)^n}$

Gaussian Integral using contour integration with a parallelogram contour

Integral $ \int_{-\pi/2}^{\pi/2} \frac{1}{2007^x+1}\cdot \frac{\sin^{2008}x}{\sin^{2008}x+\cos^{2008}x}dx $

Evaluating $\int_{0}^{\infty} \frac{x^{3}- \sin^{3}(x)}{x^{5}} \ dx $ using contour integration

Compute the series $\sum_{n=1}^{+\infty} \frac{1}{n^3\sin(n\pi\sqrt{2})}.$

When can't a real definite integral be evaluated using contour integration?

New posts in contour-integration

contour integral with singularity on the contour

Evaluate $\int_0^{\infty} \frac{\log(x)dx}{x^2+a^2}$ using contour integration

What will be $\oint \frac{1}{\sin(πz)} dz$ over a circle of radius 1.5?

Is it possible to evaluate the integral $I=\int_0^\infty \frac{\sqrt{x}\arctan(x)}{1+x^2}dx$ with residue theorem?

Evaluate $\int_0^{2\pi} \frac{\sin^2\theta}{5+4\cos\theta}\,\mathrm d\theta$

Evaluate some integrals with hypergeometric function

Closed form for $\int_0^\infty\frac{1}{(1+x^2)^s}\,dx$ when $s\in (0.5,\infty)\setminus\mathbb{N}$

Generalised Integral $I_n=\int_0^{\pi/2} \frac{x^n}{\sin ^n x} \ \mathrm{d}x, \quad n\in \mathbb{Z}^+.$

Alternative and more direct proof that an integral is independent of a parameter

Question about finite analog of $\int_0^\infty \frac{\sin x\sinh x}{\cos (2 x)+\cosh \left(2x \right)}\frac{dx}{x}=\frac{\pi}{8}$

Prove that a square-integrable entire function is identically zero

Mellin transform of $\sin x$ aka $\int^{\infty}_0 x^{s-1}\sin x dx $ [duplicate]

Is possible to use "Feynman's trick" (differentiate under the integral or Leibniz integral rule) to calculate $\int_0^1 \frac{\ln(1-x)}{x}dx\:?$

How to solve $\int_0^{\infty}\frac{\cos{ax}}{x^3+1}dx$?

closed form of $\int_{0}^{2\pi}\frac{dx}{(a^2\cos^2x+b^2\sin^2x)^n}$

Gaussian Integral using contour integration with a parallelogram contour

Integral $ \int_{-\pi/2}^{\pi/2} \frac{1}{2007^x+1}\cdot \frac{\sin^{2008}x}{\sin^{2008}x+\cos^{2008}x}dx $

Evaluating $\int_{0}^{\infty} \frac{x^{3}- \sin^{3}(x)}{x^{5}} \ dx $ using contour integration

Compute the series $\sum_{n=1}^{+\infty} \frac{1}{n^3\sin(n\pi\sqrt{2})}.$

When can't a real definite integral be evaluated using contour integration?