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New posts in contour-integration
How to evaluate the integral $\int_{0}^{\infty}\frac{\cos {(ax)}-\cos{(b x)}}{x^2 }dx$?
complex-analysis
contour-integration
residue-calculus
Why is $\int_{[0,1]} \frac{dw}{1-wz}$ is holomorphic in unit disc?
integration
complex-analysis
proof-verification
continuity
contour-integration
How to compute $\int_0^{\infty} \frac{\sqrt{x}}{x^2-1}\mathrm dx$
complex-analysis
definite-integrals
contour-integration
An integral of rational function with third power of cosine hyperbolic function
calculus
integration
definite-integrals
contour-integration
Integral by residue - "dog bone"
complex-analysis
contour-integration
residue-calculus
How to prove error function $\mbox{erf}$ is entire (i.e., analytic everywhere)?
complex-analysis
special-functions
contour-integration
error-function
Integral with $\ln$ and rational function
contour-integration
residue-calculus
integration using residue
complex-analysis
contour-integration
contour integration of logarithm
complex-analysis
contour-integration
complex-integration
Evaluating $\int_0^\infty \frac{\cos(ax)-e^{-ax}}{x \left(x^4+b^4 \right)}dx$
complex-analysis
integration
improper-integrals
contour-integration
show that $\int_{0}^{\infty } \frac {\cos (ax) -\cos (bx)} {x^2}dx=\pi \frac {b-a} {2}$
integration
contour-integration
Evaluate $\int_0^\infty \frac{(\ln x)^2}{x^2+4} \ dx$ using complex analysis.
integration
complex-analysis
contour-integration
$\int_{-\infty}^\infty \frac{\sin (t) \, dt}{t^4+1}$ must be zero and it isn't
complex-analysis
improper-integrals
contour-integration
residue-calculus
Contour Integration $\int_0^1\frac1{\sqrt[n]{1-x^n}}dx$
complex-analysis
contour-integration
residue-calculus
Riemann's Trick with Hankel Contour
contour-integration
riemann-zeta
Integral with arctan and e: $\int_{0}^{\infty}\frac{\arctan(x^{3})}{e^{2\pi x}-1}\,\mathrm dx$
definite-integrals
contour-integration
How to evaluate$J(k) = \int_{0}^{1} \frac{\ln^2x\ln\left ( \frac{1-x}{1+x} \right ) }{(x-1)^2-k^2(x+1)^2}\text{d}x$
integration
definite-integrals
logarithms
contour-integration
polylogarithm
Closed form for $I=\int_{0}^{\infty}\frac{x^n}{x^2+u^2}\tanh(x) \, dx$
integration
definite-integrals
contour-integration
closed-form
complex-integration
Residue theorem:When a singularity on the circle (not inside the circle)
integration
complex-analysis
contour-integration
residue-calculus
cauchy-principal-value
Residue theorem with $\frac{1}{2\pi}\int_{0}^{2\pi}e^{\cos\theta}\cos(n\theta) d\theta$.
complex-analysis
contour-integration
residue-calculus
complex-integration
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