New posts in improper-integrals

Integral $\int_{-\infty}^{\infty}\frac{\cos(s \arctan(ax))}{(1+x^2)(1+a^2x^2)^{s/2}}dx$

calculus complex-analysis integration definite-integrals improper-integrals

Improper integral of $\frac{x}{e^x-1}$

calculus integration improper-integrals

Is putting absolute values around the argument of a log obtained through integration incorrect?

calculus logarithms integration improper-integrals

Evaluate the integral $\int_{0}^{+\infty}\frac{\arctan \pi x-\arctan x}{x}dx$

integration improper-integrals

Evaluate $\int_0^4 \frac{\ln x}{\sqrt{4x-x^2}} \,\mathrm dx$

calculus integration definite-integrals improper-integrals

How to calculate $ \int_{0}^{\infty} \frac{ x^2 \log(x) }{1 + x^4} $?

complex-analysis integration improper-integrals residue-calculus

Convergence of $\int_0^1\frac{f(x)}{x}dx$. [duplicate]

calculus improper-integrals

Prove that $\int_0^\infty\left(\arctan \frac1x\right)^2 \mathrm d x = \pi\ln 2$

calculus integration improper-integrals conjectures experimental-mathematics

integral of $x^2e^{-x^2}~dx$ from $-\infty$ to $+\infty$

calculus integration definite-integrals improper-integrals exponentiation

What is the value of this improper integral? $\lim_{x\rightarrow 0 } \dfrac{1}{x} \int_{x}^{2x} e^{-t^2}\,\mathrm dt$

integration improper-integrals

Integral involving logarithm: $\int_0^\infty \frac{ \ln x}{(x+a)(x+b)} dx$

calculus integration logarithms improper-integrals

Prove the improper integral of the Gamma function $\Gamma(t)$ converges for $z \in \mathbb C$ with $Re(z) > 0$:

integration complex-analysis improper-integrals

Solving an integral involving exponential functions $\int_{-\infty}^{+\infty} \frac{1}{\left(e^x+ e^{-x}\right)^n} e^{-\rho x^2 + a x} dx$

integration improper-integrals exponential-function approximate-integration

Integral $ \int_0^\infty \frac{\ln x}{(x+c)(x-1)} dx$

calculus integration definite-integrals contest-math improper-integrals

Emergence of Cauchy Principal value

integration ordinary-differential-equations improper-integrals cauchy-principal-value

Closed form of an improper integral to solve the period of a dynamical system

integration improper-integrals special-functions lambert-w elliptic-integrals

Evaluate $\int\limits_0^\infty \frac{\ln^2(1+x)}{1+x^2}\ dx$

real-analysis calculus integration improper-integrals polylogarithm

Proving that $(-1)^{n+1}G_n =\int_0^\infty \frac{1}{(1+x)^n (\pi^2+\ln^2 x)} dx$

integration definite-integrals improper-integrals alternative-proof

Does Leibniz's rule hold for improper integrals?

calculus integration improper-integrals

Finding $\int_{0}^{\pi/2} \frac{\tan x}{1+m^2\tan^2{x}} \mathrm{d}x$

calculus real-analysis integration definite-integrals improper-integrals