New posts in integration

If $f$ is a positive, monotone decreasing function, prove that $\int_0^1xf(x)^2dx \int_0^1f(x)dx\le \int_0^1f(x)^2dx \int_0^1xf(x)dx$

calculus real-analysis integration inequality

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

How to integrate $\exp\left(-ax^2\right)\operatorname{erf}(bx+c)$?

integration

How to integrate the dilogarithms?

calculus integration sequences-and-series special-functions polylogarithm

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

calculus integration definite-integrals improper-integrals

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

Evaluate $\int \sqrt{ \frac {\sin(x-\alpha)} {\sin(x+\alpha)} }\,\operatorname d\!x$?

calculus integration indefinite-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

Integral becomes improper after a substitution

calculus integration improper-integrals transformation substitution

Calculate the maximum value

real-analysis calculus linear-algebra integration maxima-minima

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

Deriving Mean and Variance of Laplace Distribution

calculus integration statistics probability-distributions improper-integrals

Why does my professor say that writing $\int \frac 1x \mathrm{d}x = \ln|x| + C$ is wrong?

calculus integration logarithms indefinite-integrals

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

A numerical evaluation of $\sum_{n=1}^{\infty}(-1)^{\frac{n(n+1)}{2}}\frac1{n!}\int_0^1x^{(n)} dx$

calculus integration sequences-and-series numerical-methods mathematica

Solving the integral $\int x\sqrt{1+x}\ dx $ [closed]

integration substitution