New posts in improper-integrals

Finding constant to make integrals converge

integration definite-integrals improper-integrals

Finding $\int_0^\infty \frac{\cos(ax)-\cos(bx)}{x}dx$ [duplicate]

calculus integration definite-integrals improper-integrals

The other ways to calculate $\int_0^1\frac{\ln(1-x^2)}{x}dx$

calculus real-analysis integration definite-integrals improper-integrals

Prove $\int_0^{\infty}\frac{\ln (x)}{(x^2+1)(x^3+1)}\ dx=-\frac{37}{432}\pi^2$ with real method

calculus integration complex-analysis improper-integrals residue-calculus

Compute $\int_0^1 \frac{\arcsin(x)}{x}dx$

calculus integration trigonometry definite-integrals improper-integrals

Integral of the form $\int_0^\infty \exp{\left(-\frac{(a+bx)^2}{x}\right)}\frac{dx}{\sqrt{x^3}}$

calculus integration definite-integrals improper-integrals

hurwitz zeta Integral representation

integration improper-integrals special-functions riemann-zeta

Contour Integration of Logarithmic Rational Function

integration improper-integrals contour-integration

Need help with $\int_0^\infty\frac{e^{-x}}{\sqrt[3]2+\cos x}dx$

calculus integration definite-integrals improper-integrals closed-form

Evaluating $\int_0^{\infty}\frac{e^{-x}}{1+x^2}dx$

calculus integration improper-integrals

Evaluating $\int_0^1 \frac{z \log ^2\left(\sqrt{z^2+1}-1\right)}{\sqrt{1-z^2}} \, dz$

calculus real-analysis integration definite-integrals improper-integrals

Compute $\int_0^\infty\frac{\cos(xt)}{1+t^2}dt$

improper-integrals

Evaluate $\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{-\frac{1}{2}(x^2-xy+y^2)}dx\, dy$

real-analysis integration multivariable-calculus definite-integrals improper-integrals

$\int_{0}^{\pi/2} \text{arctanh}(\sin x) \text{arctan}(a \tan(x)) \cos(x) \ dx$

improper-integrals

Prove this integral $\int_0^\infty \frac{dx}{\sqrt{x^4+a^4}+\sqrt{x^4+b^4}}=\frac{\Gamma(1/4)^2 }{6 \sqrt{\pi}} \frac{a^3-b^3}{a^4-b^4}$

integration definite-integrals improper-integrals means beta-function

Proving a formula for $\int_0^\infty \frac{\log(1+x^{4n})}{1+x^2}dx $ if $n=1,2,3,\cdots$

analysis integration improper-integrals closed-form

Prove that $\int_0^{\infty} \frac{\sin x}{x^p}\, dx$ converges for $0<p<2$

limits proof-verification convergence-divergence improper-integrals

Limit of integral with Parseval

limits improper-integrals fourier-transform gaussian-integral parsevals-identity

Prove $\pi^2\int_0^\infty\frac{x\sin^4\pi x}{\cos\pi x+\cosh\pi x}dx=e^2\int_0^\infty\frac{x\sin^4ex}{\cos ex+\cosh ex}dx=\frac{176}{225}$

calculus integration proof-verification definite-integrals improper-integrals

Integral $\int_0^\infty\exp\left(-\sqrt2\,x^2\right)\,\operatorname{erfi}(x)\,\log(x)\,x^3\,dx$

integration improper-integrals closed-form hypergeometric-function error-function