New posts in integration

Gaussian integral with error function

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

Proving $\int_0^\pi \frac{\log(1+x\cos (y))}{\cos y}dy=\pi \arcsin x$

calculus real-analysis integration

Evaluating a Lebesgue Integral

real-analysis integration definite-integrals lebesgue-integral

Is there an elementary proof that $\int_0^{\infty}|\sin(x)|^{x}\ dx$ converges or diverges?

integration convergence-divergence improper-integrals

Asymptotic expansion of the integral $\int_0^1 e^{x^n} dx$ for $n \to \infty$

integration asymptotics

How find this integral $I=\int_{-1}^{1}\frac{dx}{\sqrt{a^2+1-2ax}\sqrt{b^2+1-2bx}}$

integration

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

Airy function value and derivative value at 0

integration contour-integration gamma-function airy-functions

Question regarding a proof from previous post.

real-analysis integration riemann-sum

Integral in $n-$dimensional euclidean space

real-analysis integration analysis definite-integrals special-functions

is there a nicer way to $\int e^{2x} \sin x\, dx$?

calculus integration indefinite-integrals

Prove $\int_0^1\frac{\ln2-\ln\left(1+x^2\right)}{1-x}\,dx=\frac{5\pi^2}{48}-\frac{\ln^22}{4}$

real-analysis calculus integration definite-integrals improper-integrals

Calculus Integration Based Proof that the Volume of a Parallelepiped spanned by $\{v_1, \ldots, v_n\}$ is $\text{det}(v_1, \ldots, v_n)$?

calculus integration linear-transformations determinant volume

Find the principal value of $\int_{-\infty}^{\infty}\frac{1-\cos x}{x^2}\,\mathrm dx$

calculus integration improper-integrals complex-integration cauchy-principal-value

Evaluating $\lim_{n\rightarrow\infty} \int_{0}^{\pi} \frac {\sin x}{1+ \cos^2 (nx)} dx$

real-analysis integration limits proof-verification definite-integrals

How to show the following integral $\int_0^\frac{\pi}{2} \cot^{-1}{\sqrt{1+\csc{\theta}}}\,\mathrm d\theta =\frac{\pi^2}{12}$

calculus integration definite-integrals improper-integrals

Smart Integration Tricks [closed]

integration definite-integrals indefinite-integrals

Prove that: $\int_{0}^{1} \frac{x^{4}\log x}{x^2-1}\le \frac{1}{8}$

real-analysis integration inequality