New posts in integration

An interesting integral with log: $\int_{0}^{\pi/2}\ln^2\left(\tan^2\left({x\over 2}\right)\right)\mathrm dx=\frac{\pi^3}2$ [closed]

real-analysis integration definite-integrals closed-form

show $\int_0^{\infty} \frac{x\sin ax}{x^2+t^2}dx = \frac{\pi}{2}e^{-at}$

integration measure-theory definite-integrals

How to evaluate this notoriously hard exponential integral

calculus integration probability-distributions

One Question about the Fubini's Theorem

calculus real-analysis integration multivariable-calculus

How to integrate $f(x) =\exp(-ax-b/x)$?

calculus integration definite-integrals improper-integrals

Anti-derivative of continuous function $\frac{1}{2+\sin x}$

calculus integration

Uniqueness of a function that satisfies a condition

integration indefinite-integrals laplace-transform

How to integrate $\int \frac{\cos^m x}{\cos nx} \,\mathrm{d}x$

integration indefinite-integrals

If $f$ is integrable, then I can bring continuous functions from above or below

real-analysis integration riemann-integration

Theorem 6.16 in Baby Rudin: $\int_a^b f d \alpha = \sum_{n=1}^\infty c_n f\left(s_n\right)$

real-analysis integration analysis proof-verification definite-integrals

How to show that $\int_{0}^{\infty}{\sin(x)\sin(2x)\sin(4x)\cdots\sin(2^kx)\over x^{k+1}}\mathrm dx=2^{0.5(k^2-k-2)}\pi?$

Area of a mushroom-shaped curve

integration definite-integrals recreational-mathematics

Generalizing Archimedes' "The Quadrature of the Parabola"

calculus integration geometry ordinary-differential-equations integral-equations

Reconciling measure-theoretic definition of expectation versus expectation defined in elementary probability

integration probability-theory random-variables definition lebesgue-integral

How do you evaluate the integral $\int\frac{x^2-1}{(x^4+3 x^2+1) \tan^{-1}\left(\frac{x^2+1}{x}\right)}\,dx$?

Use Stokes's Theorem to show $\oint_{C} y ~dx + z ~dy + x ~dz = \sqrt{3} \pi a^2$

integration multivariable-calculus

Integral $\int_0^\infty \frac{x-\sin x}{x^3(x^2+4)} dx$

integration proof-verification definite-integrals

How do I evaluate this integral :$\int \frac{1}{ \sqrt{1-x^2} } \arctan( \frac{\sqrt{1-x^2}}{2})dx$?

calculus integration trigonometry indefinite-integrals

Integral of exponential function with polynomial argument

integration exponential-function

Calculate $\int_0^\infty\frac{\sin^3{x}}{e^x-1}\mathrm dx$

calculus integration complex-analysis