New posts in definite-integrals

Help to evaluate $\int_{0}^{\pi}\sec(x)\sqrt{\tan\left(\frac{x}{2}\right)}\ln^n\tan\left(\frac{x}{2}\right)dx$

calculus integration definite-integrals trigonometric-integrals

Integral $\int_0^1 \frac{\ln(1+x)}{1+x^3}dx$

integration definite-integrals closed-form

Prove $\int_a^b \frac{1}{x}\sqrt{-(x-a)(x-b)}dx = (\frac{a+b}{2}-\sqrt{ab})\pi$

integration definite-integrals

Integrating a 'twisted' rational function

integration definite-integrals infinite-product

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

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

integration definite-integrals

unexpected high precision of the Simpson's rule

definite-integrals numerical-methods computational-mathematics

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

calculus integration trigonometry definite-integrals 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

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

Integral with exp and erf

calculus special-functions definite-integrals

Is there a closed form for $\int_a^b\frac{{\rm arccosh}x}{\sqrt{(x-a)(b-x)}}$?

real-analysis integration sequences-and-series definite-integrals closed-form

How to show $\int_{\mathbb{R}}{t \choose x}^2{x \choose t}~dx = 1$

integration definite-integrals binomial-coefficients gamma-function

Evaluating the integral $\int_{-\ln 2}^{\ln 2} e^{-x}(\sin x+x)^{1/3}dx$

integration definite-integrals

Generalization of $\int_0^\alpha \sqrt{1+\cos^2\theta}\,d\theta>\sqrt{\alpha^2+\sin^2\alpha}$

calculus definite-integrals solution-verification

$\int\text{e}^{-ax^2 } \text{erf}\left(bx + c\right) dx$

calculus integration definite-integrals indefinite-integrals error-function

Integration of exponential and square root function

calculus integration complex-analysis definite-integrals

Evaluate $\int_{(0,\infty)^n}\text{Sinc}(\sum_{k=1}^nx_k) \prod_{k=1}^n \text{Sinc}(x_k) dx_1\cdots dx_n$

integration definite-integrals