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New posts in contour-integration
Evaluate the integral $\int_0^\infty \frac{x (\ln(x))^2}{x^4 + x^2 + 1}\text{ d}x$
complex-analysis
definite-integrals
contour-integration
How does contour integral work?
contour-integration
Airy function value and derivative value at 0
integration
contour-integration
gamma-function
airy-functions
Computing $\int_0^\infty\mathrm{d} x\frac{x}{e^x+1}$ with contour integration
definite-integrals
contour-integration
An intuitive definition of contour integration.
soft-question
contour-integration
Complex analysis: contour integration
complex-analysis
integration
contour-integration
Show that $\int_1^{\infty } \frac{(\ln x)^2}{x^2+x+1} \, dx = \frac{8 \pi ^3}{81 \sqrt{3}}$
calculus
definite-integrals
improper-integrals
contour-integration
closed-form
Evaluate the integral $I=\int_{0}^{\infty}\frac{\ln^3{x}}{(1+x^2)(1+x)^2}dx$
integration
contour-integration
Contour Integral $ \int_{0}^1 \frac{\ln{x}}{\sqrt{1-x^2}} \mathrm dx$
complex-analysis
definite-integrals
logarithms
contour-integration
branch-cuts
Compute multivariate complex Gaussian integral
calculus
complex-analysis
contour-integration
gaussian-integral
Evaluating $\int\limits_0^\infty \frac{\log x} {(1+x^2)^2} dx$ with residue theory
complex-analysis
integration
contour-integration
residue-calculus
Prove $\int_0^\infty\Big|\Gamma\Big(\frac13+\frac{i\alpha}{\pi}\Big)\Big|^6\alpha \sinh\alpha~d\alpha=\frac{\pi\sqrt{27}}{4}\Gamma^9\Big(\frac23\Big)$
complex-analysis
definite-integrals
special-functions
contour-integration
alternative-proof
Trying to compute limit of singular integrals : $L= \lim_{s\to 1}(1-s)\int_{\Omega}\frac{(u(x)-u(y))}{|x-y|^{d+2s}} d y.$
real-analysis
partial-differential-equations
contour-integration
greens-theorem
singular-integrals
Using residue theorem to calculate following integral
integration
complex-analysis
analysis
contour-integration
residue-calculus
Contour integration with branch points inside the contour.
integration
complex-analysis
special-functions
laplace-transform
contour-integration
Integral $I=\int_0^\infty \frac{\ln(1+x) \operatorname{Li}_2 (-x)}{x^{3/2}} dx$
real-analysis
integration
definite-integrals
special-functions
contour-integration
Modification of Schwarz-Christoffel integral
complex-analysis
contour-integration
conformal-geometry
Complex keyhole contour integral
complex-analysis
contour-integration
complex-integration
Area integral over complex plane of non-holomorphic gaussian $e^{-z\bar{z}}$
complex-analysis
contour-integration
residue-calculus
complex-integration
Arc contribution in $\int_{-\infty}^\infty \mathrm{d}z \frac{e^{-z^2}}{z-1}$
integration
complex-analysis
improper-integrals
contour-integration
residue-calculus
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