New posts in definite-integrals

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

calculus integration definite-integrals harmonic-numbers polylogarithm

How to "fix" $\int_{-1}^1 \frac {dx}{x^2}$ with complex numbers?

calculus integration definite-integrals complex-numbers improper-integrals

Math competition problem, prove that $\int_{-\infty}^\infty e^{-\pi x^2 \left(\frac{\alpha +x}{\beta +x}\right)^2}dx=1~$ for $~0<\beta<\alpha$.

calculus integration definite-integrals contest-math closed-form

Computing $\int \sqrt{x\sqrt[3]{x\sqrt[4]{x\sqrt[5]{x\cdots}}}} \,\mathrm{d}x$

sequences-and-series definite-integrals

Algorithms for symbolic definite integration?

abstract-algebra definite-integrals computer-algebra-systems symbolic-computation

Fourier transform of squared exponential integral $\operatorname{Ei}^2(-|x|)$

calculus integration definite-integrals fourier-analysis special-functions

Lower bound on $\int_0^{\pi/4}\sin(\tan x)dx$

integration definite-integrals taylor-expansion

Compute the trigonometric integrals

calculus real-analysis definite-integrals

Solving higher order logarithms integrals without the beta function

calculus integration definite-integrals special-functions

Other integral related to Ahmed's integral

calculus integration definite-integrals improper-integrals closed-form

difficult integral $\int_0^{\pi/2}\frac{x^2({1+\tan x})^2}{\sqrt{\tan x}({1-\tan x})}\sin{4x}dx$ [closed]

integration definite-integrals

Changing signs of integration limits

integration analysis definite-integrals

Convergence of $ I=\int_0^\infty \sin x\sin(x^2)\mathrm{d}x$

calculus integration definite-integrals improper-integrals

Simplifying $\int_0^1 x^{a-1} (1-x)^{b-1} \, _2F_1\left(1,d;c+d+1;2-\frac{1}{x}\right) \, dx$

statistics definite-integrals hypergeometric-function beta-function

Proving $\sum _{k=1}^n \frac{(-1)^{k-1} 16^k (k-1)! k! (k+n-1)!}{((2 k)!)^2 (n-k)!}=\frac{4}{n}\sum _{k=1}^n \frac{1}{2 k-1}$

integration definite-integrals summation special-functions

Trying to evaluate $\int_{0}^{\infty}\frac{\ln(1+x^3)}{1+x^3}\frac{dx}{1+x^3}$

calculus integration definite-integrals trigonometric-integrals

How do Integral Transforms work

definite-integrals linear-transformations laplace-transform fourier-transform inverse-laplace

Why do the Borwein integrals stop being $\frac{\pi}{2}$?

reference-request definite-integrals divergent-series

Why should we get rid of indefinite integration?

integration definite-integrals indefinite-integrals

Evaluate integral $\int_0^\pi \sin^4\left(x+\sin 3x\right)dx$

calculus integration definite-integrals