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Closed form for $\int_1^\infty\int_0^1\frac{\mathrm dy\,\mathrm dx}{\sqrt{x^2-1}\sqrt{1-y^2}\sqrt{1-y^2+4\,x^2y^2}}$

A Mathematical Coincidence, or more?

Efficient/faster methods to find the general closed form of $\int _0^1\frac{\ln \left(ax^2+b\right)}{x+1}\:dx$

Improper integral with log and absolute value: $\int^{\infty}_{0} \frac{\log |\tan x|}{1+x^{2}} \, dx$

Does $\int_0^\infty \sin^2 (x^2)\, dx$ converge or diverge?

Integration of $\int_0^{\pi/2}\frac{d\theta}{a^2+b^2\cos^2(\theta)}$ gives results such that $\tan(\pi/2)$ comes which is "undefined". How to proceed?

Finding $\int^1_0 \frac{\log(1+x)}{x}dx$ without series expansion

Evaluating $\int_{0}^{\infty}{\sin(x)\sin(2x)\sin(3x)\ldots \sin(nx)\sin(n^{2}x) \over x^{n + 1}}\,dx $

Using differentiation under integral sign to calculate a definite integral

What are other methods to evaluate $\int_0^1 \sqrt{-\ln x} \ \mathrm dx$

Characteristic function of the normal distribution

Evaluate ${\int_0^\infty e^{-t} \log(\cos^2 t)}\,\mathrm dt$

Evaluate $\int_0^1\frac{\ln(1-x)}{x}\text{Li}_3\left(\frac{1+x}{2}\right)dx$ , $\int_0^1\frac{\ln^2(1-x)}{x}\text{Li}_2\left(\frac{1+x}{2} \right)dx$

Evaluating the integral $\int_0^{\frac{\pi}{2}}\log\left(\frac{1+a\cos(x)}{1-a\cos(x)}\right)\frac{1}{\cos(x)}dx$ [duplicate]

Elegant proof of $\int_{-\infty}^{\infty} \frac{dx}{x^4 + a x^2 + b ^2} =\frac {\pi} {b \sqrt{2b+a}}$?

New posts in improper-integrals

Divergence of an integral related to a Riemann integral $\int_{1}^{\infty}\dfrac{1}{x}dx$

Improper Integral Calculation with Lots of Constants

Solve $\int_{0}^{\infty}\ln\Big(\frac{\sin^2(x)}{x^2}+1\Big)dx=?$

Improper Riemann integral of bounded function is proper integral

Residue Integral: $\int_0^\infty \frac{x^n - 2x + 1}{x^{2n} - 1} \mathrm{d}x$

Closed form for $\int_1^\infty\int_0^1\frac{\mathrm dy\,\mathrm dx}{\sqrt{x^2-1}\sqrt{1-y^2}\sqrt{1-y^2+4\,x^2y^2}}$

A Mathematical Coincidence, or more?

Efficient/faster methods to find the general closed form of $\int _0^1\frac{\ln \left(ax^2+b\right)}{x+1}\:dx$

Improper integral with log and absolute value: $\int^{\infty}_{0} \frac{\log |\tan x|}{1+x^{2}} \, dx$

Does $\int_0^\infty \sin^2 (x^2)\, dx$ converge or diverge?

Integration of $\int_0^{\pi/2}\frac{d\theta}{a^2+b^2\cos^2(\theta)}$ gives results such that $\tan(\pi/2)$ comes which is "undefined". How to proceed?

Finding $\int^1_0 \frac{\log(1+x)}{x}dx$ without series expansion

Evaluating $\int_{0}^{\infty}{\sin(x)\sin(2x)\sin(3x)\ldots \sin(nx)\sin(n^{2}x) \over x^{n + 1}}\,dx $

Using differentiation under integral sign to calculate a definite integral

What are other methods to evaluate $\int_0^1 \sqrt{-\ln x} \ \mathrm dx$

Characteristic function of the normal distribution

Evaluate ${\int_0^\infty e^{-t} \log(\cos^2 t)}\,\mathrm dt$

Evaluate $\int_0^1\frac{\ln(1-x)}{x}\text{Li}_3\left(\frac{1+x}{2}\right)dx$ , $\int_0^1\frac{\ln^2(1-x)}{x}\text{Li}_2\left(\frac{1+x}{2} \right)dx$

Evaluating the integral $\int_0^{\frac{\pi}{2}}\log\left(\frac{1+a\cos(x)}{1-a\cos(x)}\right)\frac{1}{\cos(x)}dx$ [duplicate]

Elegant proof of $\int_{-\infty}^{\infty} \frac{dx}{x^4 + a x^2 + b ^2} =\frac {\pi} {b \sqrt{2b+a}}$?