Newbetuts

A suprising conjectural closed-form of $\sum _{n=1}^{\infty } \frac{1}{n^4 2^n \binom{3 n}{n}}$ and integral variations

Prove that $\int_{0}^{+\infty} u^{s-1} \cos (a u) \:e^{-b u}\:du=\frac{\Gamma(s)\cos\left(s\arctan \left(\frac{a}{b}\right)\right)}{(a^2+b^2)^{s/2}}$

Why does 'The King Property' of integration work?

Compute $\int_0^\infty \frac{\operatorname{Li}_3(x)}{1+x^2}\ dx$

Infinite summation of recursive integral

Closed Form for $\int_0^1 \frac{\log(x)}{\sqrt{1-x^2}\sqrt{x^2+2+2\sqrt{2}}}dx$

Relations between definite integrals not having a known closed form

More on the integral $\int_0^1\int_0^1\int_0^1\int_0^1\frac{1}{(1+x) (1+y) (1+z)(1+w) (1+ x y z w)} \ dx \ dy \ dz \ dw$

A logarithmic integral, generalization of a result of Shalev

Examining $\int_0^1 \left(\frac{x - 1}{\ln(x)} \right)^n\:dx$

Close-form for integral $T(n)=\int_0^{\pi/2}\frac{1}{1+\sin^n(x)}dx$

Calculate $\int_0^1 \frac{\ln(1-x+x^2)}{x-x^2}dx$

Find closed form for quadruple integral

Triple Integral $ \iiint\limits_S\frac1{\sqrt{\left(x-a\right)^{2}+\left(y-b\right)^{2}+\left(z-c\right)^{2}}}\;dx\;dy\;dz $

Approximating $\int_1^{10}x^x\mathrm dx$ to within 5% relative error

Evaluating some Limits as Riemann sums.

New posts in definite-integrals

Calculating an integral related to the Gamma function [duplicate]

Evaluate $\int_{0}^{\frac{\pi}{4}}\ln(\cos(t))dt$

Compute $\lim_{s\to 0} \left(\int_0^1 (\Gamma (x))^s\space\mathrm{dx}\right)^{1/s}$

Help with a troublesome double integral

A suprising conjectural closed-form of $\sum _{n=1}^{\infty } \frac{1}{n^4 2^n \binom{3 n}{n}}$ and integral variations

Prove that $\int_{0}^{+\infty} u^{s-1} \cos (a u) \:e^{-b u}\:du=\frac{\Gamma(s)\cos\left(s\arctan \left(\frac{a}{b}\right)\right)}{(a^2+b^2)^{s/2}}$

Why does 'The King Property' of integration work?

Compute $\int_0^\infty \frac{\operatorname{Li}_3(x)}{1+x^2}\ dx$

Infinite summation of recursive integral

Closed Form for $\int_0^1 \frac{\log(x)}{\sqrt{1-x^2}\sqrt{x^2+2+2\sqrt{2}}}dx$

Relations between definite integrals not having a known closed form

More on the integral $\int_0^1\int_0^1\int_0^1\int_0^1\frac{1}{(1+x) (1+y) (1+z)(1+w) (1+ x y z w)} \ dx \ dy \ dz \ dw$

A logarithmic integral, generalization of a result of Shalev

Examining $\int_0^1 \left(\frac{x - 1}{\ln(x)} \right)^n\:dx$

Close-form for integral $T(n)=\int_0^{\pi/2}\frac{1}{1+\sin^n(x)}dx$

Calculate $\int_0^1 \frac{\ln(1-x+x^2)}{x-x^2}dx$

Find closed form for quadruple integral

Triple Integral $ \iiint\limits_S\frac1{\sqrt{\left(x-a\right)^{2}+\left(y-b\right)^{2}+\left(z-c\right)^{2}}}\;dx\;dy\;dz $

Approximating $\int_1^{10}x^x\mathrm dx$ to within 5% relative error

Evaluating some Limits as Riemann sums.