New posts in definite-integrals

Can the integral of a function be larger than function itself?

real-analysis convergence-divergence definite-integrals

Volume of a pyramid, using an integral

calculus integration definite-integrals solid-geometry

Proving $\int_0^1 \frac{(\ln(x))^5}{1+x} \mathrm{d}x = -\frac{31\pi^6}{252}$

calculus integration definite-integrals contour-integration closed-form

Evaluate $\int_0^\infty \frac{\arctan(3x) - \arctan(9x)}{x} {dx}$

calculus integration definite-integrals improper-integrals

Evaluate the integral $\int_0^\infty \frac{x (\ln(x))^2}{x^4 + x^2 + 1}\text{ d}x$

complex-analysis definite-integrals contour-integration

Integral ${\large\int}_0^\infty\big(2J_0(2x)^2+2Y_0(2x)^2-J_0(x)^2-Y_0(x)^2\big)\,dx$

integration definite-integrals special-functions closed-form bessel-functions

Evaluating $\int_{0}^{1}\frac{x-1}{(x+1)\ln x} dx $ [duplicate]

calculus integration definite-integrals

A definite integral with tanh and sin

integration definite-integrals

Computing $\lim_{n \to \infty} \sqrt[n]{ \int_{0}^{1} (1+x^n)^n dx}$

calculus integration limits definite-integrals

Evaluate $\int_{0}^{\pi} \frac{x\coth x-1}{x^2}dx$

calculus integration definite-integrals summation improper-integrals

Deriving an explicit form for the nested sine integral $\int_{-\infty}^t \sin\left(A\sin(\omega t)-A\sin(\omega s)\right)e^{s-t}ds$ [closed]

real-analysis calculus integration definite-integrals hypergeometric-function

Proving elementary, $\int_0^{2\pi}\log \frac{(1+\sin x)^{1+\cos x}}{1+\cos x} \mathrm{d}x=0$

integration definite-integrals improper-integrals elementary-functions symmetric-functions

Dirichlet's integral $\int_{V}\ x^{p}\,y^{q}\,z^{r}\ \left(\, 1 - x - y - z\,\right)^{\,s}\,{\rm d}x\,{\rm d}y\,{\rm d}z$

integration multivariable-calculus definite-integrals

Gaussian integral with error function

integration definite-integrals change-of-variable gaussian-integral error-function

Evaluating a Lebesgue Integral

real-analysis integration definite-integrals lebesgue-integral

A problem from the Shortlist of the Romanian Mathematics Olympiad

real-analysis inequality definite-integrals contest-math integral-inequality

Prove $\int_{0}^{1} \frac{\sin^{-1}(x)}{x} dx = \frac{\pi}{2}\ln2$

integration definite-integrals special-functions polylogarithm

Evaluating $-\int_0^1\frac{1-x}{(1-x+x^2)\log x}\,dx$

integration definite-integrals

Evaluate $\int_{0}^{1}\frac{1+x+x^2}{1+x+x^2+x^3+x^4}dx$

integration definite-integrals

Integral in $n-$dimensional euclidean space

real-analysis integration analysis definite-integrals special-functions