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New posts in definite-integrals
Is there an analytical solution to $\int_1^\infty \frac {dx}{\prod_{i=0}^n (x+i)}$
definite-integrals
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 $f\left(0\right)$
calculus
definite-integrals
contest-math
About the integral $\int_{0}^{1}\text{arctanh}(x)\arcsin(x)\frac{dx}{x}$
definite-integrals
fourier-series
special-functions
hypergeometric-function
Solving $\int_0^{\frac{\pi}{2}}\frac{1}{\sin^{2n}(x) + \cos^{2n}(x)}\:dx$
integration
definite-integrals
gamma-function
trigonometric-integrals
beta-function
General integral $\int_0^{\frac{\pi}{p}}\ln\tan x \,dx $
inequality
definite-integrals
special-functions
closed-form
Can $\int_{2}^{\infty} [\zeta(x)-1] dx $ be evaluated?
definite-integrals
analytic-number-theory
riemann-zeta
Computation of $\int_0^1 \frac{\arctan^2 x\ln x}{1+x}dx$
integration
definite-integrals
catalans-constant
$\frac{1}{e^x-1}$, $\Gamma(s)$, $\zeta(s)$, and $x^{s-1}$
special-functions
definite-integrals
Calculating 2 integrals in polylogarithmic functions
calculus
real-analysis
integration
definite-integrals
On the evaluation of the integral $\int_{-\frac{b}{a}}^{\frac{1-b}{a}}\log\left(ax+b\right)\exp\left(-\frac{1}{2}x^2\right)\mathrm{d}x$.
integration
definite-integrals
normal-distribution
Prove that $f(ax + (1-a)y) = \frac{1}{y-x}\int_x^y f(t)dt$ implies $a = \frac{1}{2}$
real-analysis
integration
definite-integrals
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]
inequality
definite-integrals
integral-inequality
An $\operatorname{erfi}(x)e^{-x^2}$ integral
calculus
integration
definite-integrals
special-functions
Why is arc length not in the formula for the volume of a solid of revolution?
calculus
integration
definite-integrals
How to find the value of $I_1=\int_0^\infty\frac{\sqrt{x}\arctan{x}\log^2({1+x^2})}{1+x^2}dx$
calculus
integration
definite-integrals
improper-integrals
closed-form
Accuracy of the radiocarbon method (from a mathematical point of view)
integration
definite-integrals
exponential-function
physics
Reduction formula for integral $\sin^m x \cos^n x$ with limits $0$ to $\pi/2$
definite-integrals
Solution to the "near-Gaussian" integral $\int_{0}^{\infty} e^{- \Lambda \sqrt{(z^2+a)^2+b^2}}\mathrm{d}z$
integration
definite-integrals
improper-integrals
Prove that: $ \int_{0}^{1} \ln \sqrt{\frac{1+\cos x}{1-\sin x}}\le \ln 2$
calculus
real-analysis
integration
inequality
definite-integrals
How to prove $\int_1^\infty\frac{K(x)^2}x dx=\frac{i\,\pi^3}8$?
complex-analysis
definite-integrals
special-functions
closed-form
elliptic-integrals
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