New posts in improper-integrals

Dirac delta function of non-linear multivariable arguments

integration definite-integrals improper-integrals distribution-theory dirac-delta

Closed form of $\int_0^{\infty} \frac{\log(x)}{\cosh(x) \sec(x)- \tan(x)} \ dx$

calculus real-analysis integration definite-integrals improper-integrals

Evaluate $\int_1^\infty \frac {dx}{x^3+1}$

integration complex-analysis definite-integrals improper-integrals contour-integration

Integrating : $\int_0^1 {\frac {x^a-x^b} {\ln x} dx}$ [duplicate]

calculus real-analysis integration definite-integrals improper-integrals

Closed form for $\int_1^\infty\frac{\operatorname dx}{\operatorname \Gamma(x)}$

calculus integration improper-integrals closed-form gamma-function

Difficult integral involving $\arctan x$

integration definite-integrals improper-integrals

Evaluate $\int_0^1 \frac{\ln (1 - x) \ln (1 + x)}{x} \, dx$

integration definite-integrals improper-integrals euler-sums

Derive Dirichlet test from Abel test

real-analysis integration sequences-and-series improper-integrals

Calculating $\int_0^\infty \frac {\sin^2x}{x^2}dx$ using the Residue Theorem. [duplicate]

integration complex-analysis definite-integrals improper-integrals residue-calculus

Prove that $\int_{0}^{\infty}{1\over x^4+x^2+1}dx=\int_{0}^{\infty}{1\over x^8+x^4+1}dx$

calculus integration proof-verification definite-integrals improper-integrals

How was the difference of the Fransén–Robinson constant and Euler's number found?

improper-integrals gamma-function transcendental-numbers constants

How to prove that $\int_{0}^{\infty}\sin{x}\arctan{\frac{1}{x}}\,\mathrm dx=\frac{\pi }{2} \big(\frac{e-1}e\big)$

calculus integration definite-integrals improper-integrals

Integrating $\int_0^{\frac{\pi}{2}} x (\log\tan x)^{2n+1}\;dx$

integration definite-integrals improper-integrals

For which values of $\alpha$ and $\beta$ does the integral $\int\limits_2^{\infty}\frac{dx}{x^{\alpha}\ln^{\beta}x}$ converge?

calculus integration definite-integrals improper-integrals

integral $\int_{0}^{\infty}\frac{\cos(\pi x^{2})}{1+2\cosh(\frac{2\pi}{\sqrt{3}}x)}dx=\frac{\sqrt{2}-\sqrt{6}+2}{8}$

integration complex-analysis definite-integrals improper-integrals contour-integration

How do I solve this improper integral: $\int_{-\infty}^\infty e^{-x^2-x}dx$?

calculus integration definite-integrals improper-integrals

Under what conditions is integrating over a series expansion valid for an improper integral?

sequences-and-series taylor-expansion improper-integrals

Closed form of $\int_0^\infty \left(\frac{\arctan x}{x}\right)^ndx$

integration definite-integrals improper-integrals

Integral $\int_{-\infty}^{\infty} \arctan(e^x) \arctan(e^{-x})dx=\frac{7}{4}\zeta(3)$

integration definite-integrals improper-integrals riemann-zeta trigonometric-integrals

Evaluating $\int_{0}^{\infty}\frac{\sin(ax)}{\sinh(x)}dx$ with a rectangular contour

integration complex-analysis improper-integrals contour-integration residue-calculus