New posts in integration

What is the sign of the integral $\int_{0}^{2\pi}e^{\sin(x)}\cos(nx)\,dx$?

real-analysis integration complex-analysis definite-integrals recurrence-relations

Evaluation of $ \int\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}dx$

calculus integration indefinite-integrals

Show that if $f$ is continuous on [0,1], then: $\int_0^\frac\pi 2 f(\sin x)dx=\int_0^\frac\pi 2 f(\cos x)dx= \frac12\int_0^\pi f(\sin x)dx$

calculus integration analysis

transformation of integral from 0 to infinity to 0 to 1

integration transformation monte-carlo

Integral $\int_{-\infty}^{\infty}\frac{\sin(x-\frac{a}{x})}{(x+\frac{1}{x})}dx$ [closed]

integration definite-integrals

integrals involving minimum function

calculus integration

Show that $\int_0^{\infty}\frac{f(ax)-f(bx)}{x}dx=[f(0)-L]\ln\frac{b}{a}$ [duplicate]

real-analysis integration improper-integrals

Change of variables for a Dirac delta function

integration notation distribution-theory dirac-delta

Taking the derivative inside the integral (Liebniz Rule for differentiation under the integral sign)

calculus integration derivatives

Why aren't there two equivalent ways to set up the limits of integraion for P(X>Y)?

calculus probability integration statistics multivariable-calculus

Integrate $I(a) = \int_0^{\pi/2} \frac{dx}{1-a\sin x}$

calculus integration trigonometry definite-integrals closed-form

Evaluating the limit of a certain definite integral

calculus real-analysis integration limits closed-form

A reason for the value of $\int_{0}^{1}\log{(x)}\log{(1-x)}\,\mathrm{d}x$

calculus integration definite-integrals soft-question logarithms

Evaluating $~\int_0^1\sqrt{\frac{1+x^n}{1-x^n}}~dx~$ and $~\int_0^1\sqrt[n]{\frac{1+x^2}{1-x^2}}~dx$

calculus integration definite-integrals closed-form beta-function

another product of log integral

calculus integration definite-integrals

How to prove $dxdy = r dr d \theta$?

integration multivariable-calculus

How to study the convergence of $ \int_{0}^{\infty}\frac{dx}{1+x^{2}|\sin(x)|} $?

real-analysis integration sequences-and-series improper-integrals

Pullback of a differential form by a local diffeomorphism

integration differential-geometry smooth-manifolds differential-forms pullback

Prove the following beta integral identity

integration gamma-function harmonic-analysis beta-function

Integral $\int_{-1}^{1} \frac{1}{(1+u^2)^{n/2}} \exp{\left(-2\pi \frac{a^2+b^2}{1+u^2}\right)} \exp{\left(-4\pi i ab \frac{u}{1+u^2}\right)} du $

calculus integration definite-integrals special-functions complex-integration