Newbetuts

How prove this integral $ \int\limits_0^1 \int\limits_0^1 \ln\Gamma(x+y^3)\,dx\,dy =-\frac 7 {16}+\frac{1}{2}\ln 2\pi$

Definite integral - closed form: $\int_{0}^{\infty}\cos\left(x^{4} + 1 \over x^{2}\right)\,{\rm d}x$

Evaluating $\int_{0}^{\frac{\pi}{2}} x^n \csc(x) dx$

The value of the integral $\int_0^2\left(\sqrt{1+x^3}+\sqrt[3]{x^2+2x}\:\right)dx$

Evaluating the integral $\int_0^\infty \frac{x \sin rx }{a^2+x^2} dx$ using only real analysis

Evaluating $\sum_{n=1}^\infty\frac{(H_n)^2}{n}\frac{\binom{2n}n}{4^n}$

Does $||f'||_\infty \leq \sqrt{t_F-t_0}\,||f'||_2$ hold for time-limited continuous functions $f(t)$ with $\sup_t |f'(t)|<\infty$?

Clues on how to solve these types of problems within 2-3 minutes for competitive exams

Double Integral $\int\limits_0^1\!\!\int\limits_0^1\frac{(xy)^s}{\sqrt{-\log(xy)}}\,dx\,dy$

Why solving a differentiated integral equation might eventually lead to erroneous solutions of the original problem?

Which method to use to integrate this function?

Show that $\int_{-\pi}^\pi\sin mx\sin nx d x$ is 0 $m\neq n$ and $\pi$ if $m=n$ using integration by parts

Integrating $\int^0_\pi \frac{x \sin x}{1+\cos^2 x}$

Exercise on derivative of an integral

How to solve integral $\int_0^{2\pi} e^{i(a\cos\phi + b\sin\phi)} \cos\phi\ d\phi$

Could it possibly have a nice closed form? $\int _0^1\int _0^1\frac{x y}{(x+1) (y+1) \log (x y)}\ dx \ dy$

Proof of the relation $\int^1_0 \frac{\log^n x}{1-x}dx=(-1)^n~ n!~ \zeta(n+1)$

New posts in definite-integrals

Proof that monotone functions are integrable with the classical definition of the Riemann Integral

Integral $\int_0^\infty \frac{|\sin\sqrt{qx}|-|\sin\sqrt{px}|}{x}dx$

Evaluating $\int_0^{\pi/2} \log(1 - x \cot x) \, dx\;$ (Is there a closed form?)

How prove this integral $ \int\limits_0^1 \int\limits_0^1 \ln\Gamma(x+y^3)\,dx\,dy =-\frac 7 {16}+\frac{1}{2}\ln 2\pi$

Definite integral - closed form: $\int_{0}^{\infty}\cos\left(x^{4} + 1 \over x^{2}\right)\,{\rm d}x$

Evaluating $\int_{0}^{\frac{\pi}{2}} x^n \csc(x) dx$

The value of the integral $\int_0^2\left(\sqrt{1+x^3}+\sqrt[3]{x^2+2x}\:\right)dx$

Evaluating the integral $\int_0^\infty \frac{x \sin rx }{a^2+x^2} dx$ using only real analysis

Evaluating $\sum_{n=1}^\infty\frac{(H_n)^2}{n}\frac{\binom{2n}n}{4^n}$

Does $||f'||_\infty \leq \sqrt{t_F-t_0}\,||f'||_2$ hold for time-limited continuous functions $f(t)$ with $\sup_t |f'(t)|<\infty$?

Clues on how to solve these types of problems within 2-3 minutes for competitive exams

Double Integral $\int\limits_0^1\!\!\int\limits_0^1\frac{(xy)^s}{\sqrt{-\log(xy)}}\,dx\,dy$

Why solving a differentiated integral equation might eventually lead to erroneous solutions of the original problem?

Which method to use to integrate this function?

Show that $\int_{-\pi}^\pi\sin mx\sin nx d x$ is 0 $m\neq n$ and $\pi$ if $m=n$ using integration by parts

Integrating $\int^0_\pi \frac{x \sin x}{1+\cos^2 x}$

Exercise on derivative of an integral

How to solve integral $\int_0^{2\pi} e^{i(a\cos\phi + b\sin\phi)} \cos\phi\ d\phi$

Could it possibly have a nice closed form? $\int _0^1\int _0^1\frac{x y}{(x+1) (y+1) \log (x y)}\ dx \ dy$

Proof of the relation $\int^1_0 \frac{\log^n x}{1-x}dx=(-1)^n~ n!~ \zeta(n+1)$