New posts in definite-integrals

Is there an analytical solution to $\int_1^\infty \frac {dx}{\prod_{i=0}^n (x+i)}$

If $f\left(\pi\right)=\pi$ and $\int_{0}^{\pi}\left(f\left(x\right)+f''\left(x\right)\right)\sin x\ dx\ =\ 7\pi$ then find $f\left(0\right)$

About the integral $\int_{0}^{1}\text{arctanh}(x)\arcsin(x)\frac{dx}{x}$

Solving $\int_0^{\frac{\pi}{2}}\frac{1}{\sin^{2n}(x) + \cos^{2n}(x)}\:dx$

General integral $\int_0^{\frac{\pi}{p}}\ln\tan x \,dx $

Can $\int_{2}^{\infty} [\zeta(x)-1] dx $ be evaluated?

Computation of $\int_0^1 \frac{\arctan^2 x\ln x}{1+x}dx$

$\frac{1}{e^x-1}$, $\Gamma(s)$, $\zeta(s)$, and $x^{s-1}$

Calculating 2 integrals in polylogarithmic functions

On the evaluation of the integral $\int_{-\frac{b}{a}}^{\frac{1-b}{a}}\log\left(ax+b\right)\exp\left(-\frac{1}{2}x^2\right)\mathrm{d}x$.

Prove that $f(ax + (1-a)y) = \frac{1}{y-x}\int_x^y f(t)dt$ implies $a = \frac{1}{2}$

How to prove $\int_0^1 f^2(x)\cdot f'^4(x)\ dx\leq \int_0^1 f^4(x)\cdot f''^2(x)\ dx$ [closed]

An $\operatorname{erfi}(x)e^{-x^2}$ integral

Why is arc length not in the formula for the volume of a solid of revolution?

How to find the value of $I_1=\int_0^\infty\frac{\sqrt{x}\arctan{x}\log^2({1+x^2})}{1+x^2}dx$

Accuracy of the radiocarbon method (from a mathematical point of view)

Reduction formula for integral $\sin^m x \cos^n x$ with limits $0$ to $\pi/2$

Solution to the "near-Gaussian" integral $\int_{0}^{\infty} e^{- \Lambda \sqrt{(z^2+a)^2+b^2}}\mathrm{d}z$

Prove that: $ \int_{0}^{1} \ln \sqrt{\frac{1+\cos x}{1-\sin x}}\le \ln 2$

How to prove $\int_1^\infty\frac{K(x)^2}x dx=\frac{i\,\pi^3}8$?