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Find the principal value of $\int_{-\infty}^{\infty}\frac{1-\cos x}{x^2}\,\mathrm dx$
calculus
integration
improper-integrals
complex-integration
cauchy-principal-value
Asymptotic expression of $\int_{- D}^{D} \frac{\text{tanh}(\xi)}{\xi -\omega}\mathrm{d}\xi$
calculus
integration
asymptotics
cauchy-principal-value
Residue theorem:When a singularity on the circle (not inside the circle)
integration
complex-analysis
contour-integration
residue-calculus
cauchy-principal-value
Evaluate Integral with $e^{ut}\ \Gamma (u)^{2}$
integration
sequences-and-series
laplace-transform
contour-integration
cauchy-principal-value
Integration of an improper integral and the Cauchy principal value
improper-integrals
cauchy-principal-value
pole on the contour using the residu theorem, what is this formula of Plemelj?
complex-analysis
solution-verification
residue-calculus
cauchy-principal-value
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
Help me to finish calculating $\int_0^{\infty} \frac{1}{x^3-1}dx$
calculus
integration
definite-integrals
cauchy-principal-value
Emergence of Cauchy Principal value
integration
ordinary-differential-equations
improper-integrals
cauchy-principal-value
How to find $\operatorname{P.V.}\int_0^1 \frac{1}{x (1-x)}\arctan \left(\frac{8 x^2-4 x^3+14 x-8}{2 x^4-3 x^3-11 x^2+16 x+16}\right) \textrm{d}x$?
real-analysis
calculus
integration
alternative-proof
cauchy-principal-value
contour integral with singularity on the contour
complex-analysis
contour-integration
cauchy-principal-value
What makes the Cauchy principal value the "correct" value for a integral?
integration
probability-distributions
mathematical-physics
cauchy-principal-value
About Cauchy Principal Value
calculus
integration
cauchy-principal-value
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