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New posts in contour-integration
How does the integral $\int_{D_C} e^{ia z}P(z)/Q(z)\,\mathrm{d}z$ blow up.
integration
complex-analysis
contour-integration
How to show $\int^{\infty}_{-\infty}\frac{\sin(ax)}{x(x^2+1)}dx=\pi(1-e^{-a})$? ($a\ge0$)
complex-analysis
definite-integrals
contour-integration
residue-calculus
Calculating ${\int_{-\infty}^{\infty} \frac{\cos(\omega x)}{x^{2} + 25}\,{\rm d}x}$ using contour integration
complex-analysis
definite-integrals
contour-integration
Integral $\int_0^{\infty}\frac{e^{-a x^2(x^2-\pi^2)}\cos(2\pi a x^3)}{\cosh x}dx$
calculus
integration
contour-integration
Applications of the Residue Theorem to the Evaluation of Integrals and Sums
integration
complex-analysis
improper-integrals
contour-integration
residue-calculus
An integral formula for the reciprocal gamma function
calculus
complex-analysis
factorial
contour-integration
Integrate $\int_{-\infty}^{\infty} \frac{\cosh(\beta x)}{1+\cosh( \beta x )} e^{-x^2} x^2 \rm{d}x$
complex-analysis
contour-integration
Contour method to solve $\int^\infty_0\frac{\ln(1+x)}{1+x^2}\,dx$
complex-analysis
contour-integration
How do I prove $\int_{-\infty}^{\infty}{\cos(x+a)\over (x+b)^2+1}dx={\pi\over e}{\cos(a-b)}$?
integration
definite-integrals
contour-integration
Complex integration: $ \int_{c} \frac{e^{z}}{z(z-3)} dz$
complex-analysis
contour-integration
complex-integration
cauchy-integral-formula
Evaluate Integral with $e^{ut}\ \Gamma (u)^{2}$
integration
sequences-and-series
laplace-transform
contour-integration
cauchy-principal-value
Inverse Laplace Transform of $e^{-\sqrt{s^2+s}}$.
integration
complex-analysis
laplace-transform
contour-integration
residue-calculus
How does one convert an integrand of the form $\frac{x\sinh x-t\sinh t}{\sinh^2x-\sinh^2t}$ into the form $\frac{\ln(x^2-t^2+1)}{\sinh^2x-\sinh^2t}$?
definite-integrals
logarithms
contour-integration
gamma-function
hyperbolic-functions
Finding the integral $I=\int_0^1{x^{-2/3}(1-x)^{-1/3}}dx$
integration
complex-analysis
contour-integration
Prove using contour integration that $\int_0^\infty \frac{\log x}{x^3-1}\operatorname d\!x=\frac{4\pi^2}{27}$
complex-analysis
definite-integrals
contour-integration
Calculation of $\int^{\pi/2}_{0}\cos^{n}(x)\cos (nx)\,dx$, where $n\in \mathbb{N}$
calculus
complex-analysis
contour-integration
residue-calculus
Does $\int_{0}^{\infty}{\sin{(\pi{x^2})}\over \sinh{(\pi{x}})\tanh(x\pi)}\mathrm{d}x$ have a simple closed from?
calculus
integration
definite-integrals
contour-integration
LogSine Integral $\int_0^{\pi/3}\ln^n\big(2\sin\frac{\theta}{2}\big)\mathrm d\theta$
calculus
integration
definite-integrals
improper-integrals
contour-integration
Evaluate Complex Integral with $\frac{\Gamma(\frac{s}{2})} {\Gamma\big({\beta +1\over 2} - {s\over 2}\big)}$
integration
contour-integration
complex-integration
line-integrals
cauchy-principal-value
Evaluate $\int_0^{\infty} \frac{\log x }{(x-1)\sqrt{x}}dx$ (solution verification)
complex-analysis
contour-integration
solution-verification
residue-calculus
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