New posts in improper-integrals

Convergence of $\int_0^\infty $sin$ (x^p) dx$

real-analysis integration convergence-divergence improper-integrals

Evaluating $\int_0^\infty \left| \frac{\sin t}{t} \right|^n \, \mathrm{d}t$ for $n = 3, 5, 7, \dots$

real-analysis calculus integration definite-integrals improper-integrals

Simple equivalent of $\int_0^\infty\frac{dx}{(x+1)(x+2)...(x+n)}$ when $n\to\infty$

integration definite-integrals improper-integrals

Integral representation of Bessel function $J_1(x)$

integration improper-integrals bessel-functions absolute-convergence conditional-convergence

closed form for $\int_0^{\infty}\log^n\left(\frac{e^x}{e^x-1}\right)dx$

integration definite-integrals improper-integrals closed-form

Integral of $d$ dimension Calculation

real-analysis integration complex-analysis analysis improper-integrals

How to compute $\int_0^{+\infty} \frac{dt}{1+t^4} = \frac{\pi}{2\sqrt 2}.$

calculus integration definite-integrals improper-integrals

Finding the closed form of $\int_0^1 \frac{(1-x+x\log x)\operatorname{Li}_3(x)}{x(x-1) \log x} \ dx$

calculus real-analysis integration definite-integrals improper-integrals

How to prove that $\int_{0}^{\infty}{\sin^4(x)\ln(x)}\cdot{\mathrm dx\over x^2}={\pi\over 4}\cdot(1-\gamma)?$

calculus integration improper-integrals

Show $\int_0^\infty f\left(x+\frac{1}{x}\right)\,\frac{\ln x}{x}\,dx=0$ if $f(x)$ is a bounded non-negative function

definite-integrals improper-integrals calculus real-analysis integration

Improper integrals with singularities on the REAL AXIS (Complex Variable)

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

Arctangent integral that I'm having difficulty on

integration definite-integrals improper-integrals

Why am I getting 2 different answers for Integral exp(ix) from 0 to Infinity

definite-integrals improper-integrals exponentiation complex-integration

Integral $\int_{-\infty}^{\infty}\frac{e^{r \arctan(ax)}+e^{-r \arctan(ax)}}{1+x^2}\cos \left( \frac{r}{2}\log(1+a^2x^2)\right)dx$

calculus complex-analysis integration improper-integrals

Find $\int_{0}^{\infty }\frac{\cos x-\cos x^2}{x}\mathrm dx$

integration definite-integrals improper-integrals

Calculus Question: Improper integral $\int_{0}^{\infty}\frac{\cos(2x+1)}{\sqrt[3]{x}}\text dx$

calculus real-analysis integration definite-integrals improper-integrals

Challenging problem: Find $a$ where $\int_0^\infty \frac{\cos(ax)\ln(1+x^2)}{\sqrt{1+x^2}}dx=0$.

real-analysis calculus integration improper-integrals

Evaluate $\int_0^\infty \frac{\arctan(3x) - \arctan(9x)}{x} {dx}$

calculus integration definite-integrals improper-integrals

Integral becomes improper after a substitution

calculus integration improper-integrals transformation substitution

Evaluate $\int_{0}^{\pi} \frac{x\coth x-1}{x^2}dx$

calculus integration definite-integrals summation improper-integrals