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Show that $\int_0^1 \prod_{n\geq 1} (1-x^n) \, dx = \frac{4\pi\sqrt{3}\sinh(\frac{\pi}{3}\sqrt{23})}{\sqrt{23}\cosh(\frac{\pi}{2}\sqrt{23})}$ [duplicate]

Why is this integral diverging? $\int\limits^{\infty}_{-\infty} \,\frac{x}{x^2+1} dx$

Prove the following integral is constant: $\int_{-1}^{+1} \frac{ \ln |a-x|^2 }{\sqrt{1 - x^2}} dx$

Value of this definite integral $\int_{0}^{\infty} \frac{ \ln(x)}{x^2+2x+4} dx $

Understanding Limits of Integration in Integration-by-Parts

How to evaluate $\lim_{n\rightarrow \infty }\left ( \int_{0}^{2\pi}{\frac{\cos(nx)}{x^{2}+n^{2}}}dx \right ) where\ \forall \ \ n\in \mathbb{N} $?

Integral $\int_{-\infty}^{\infty}\frac{e^{r \arctan(ax)}+e^{-r \arctan(ax)}}{1+x^2}\cos \left( \frac{r}{2}\log(1+a^2x^2)\right)dx$

Show that if $f$ is integrable on $[a,b]$, then $|f|$ is also integrable.

Remarkable integral: $\int_0^{\infty} x \left(1 - \frac{\sinh x}{\cosh x-\sqrt 3/2} \right) \mathrm dx= -\frac{13 \pi ^2}{72}$?

Integral $\int_0^{\pi/4}\log \tan x \frac{\cos 2x}{1+\alpha^2\sin^2 2x}dx=-\frac{\pi}{4\alpha}\text{arcsinh}\alpha$

Integral of rational function with higher degree in numerator

Evaluating $\int_{0}^{\pi/2}\frac{x\sin x\cos x\;dx}{(a^{2}\cos^{2}x+b^{2}\sin^{2}x)^{2}}$

Find $\int_{0}^{\infty }\frac{\cos x-\cos x^2}{x}\mathrm dx$

What is cosine to the power of zero?

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Arctangent integral that I'm having difficulty on

Integral $\int_0^\frac{\pi}{2} \arcsin(\sqrt{\sin x}) dx$

Show that $\int_0^1 \prod_{n\geq 1} (1-x^n) \, dx = \frac{4\pi\sqrt{3}\sinh(\frac{\pi}{3}\sqrt{23})}{\sqrt{23}\cosh(\frac{\pi}{2}\sqrt{23})}$ [duplicate]

Why is this integral diverging? $\int\limits^{\infty}_{-\infty} \,\frac{x}{x^2+1} dx$

Prove the following integral is constant: $\int_{-1}^{+1} \frac{ \ln |a-x|^2 }{\sqrt{1 - x^2}} dx$

Value of this definite integral $\int_{0}^{\infty} \frac{ \ln(x)}{x^2+2x+4} dx $

Understanding Limits of Integration in Integration-by-Parts

How to evaluate $\lim_{n\rightarrow \infty }\left ( \int_{0}^{2\pi}{\frac{\cos(nx)}{x^{2}+n^{2}}}dx \right ) where\ \forall \ \ n\in \mathbb{N} $?

Integral $\int_{-\infty}^{\infty}\frac{e^{r \arctan(ax)}+e^{-r \arctan(ax)}}{1+x^2}\cos \left( \frac{r}{2}\log(1+a^2x^2)\right)dx$

Show that if $f$ is integrable on $[a,b]$, then $|f|$ is also integrable.

Remarkable integral: $\int_0^{\infty} x \left(1 - \frac{\sinh x}{\cosh x-\sqrt 3/2} \right) \mathrm dx= -\frac{13 \pi ^2}{72}$?

Integral $\int_0^{\pi/4}\log \tan x \frac{\cos 2x}{1+\alpha^2\sin^2 2x}dx=-\frac{\pi}{4\alpha}\text{arcsinh}\alpha$

Integral of rational function with higher degree in numerator

Evaluating $\int_{0}^{\pi/2}\frac{x\sin x\cos x\;dx}{(a^{2}\cos^{2}x+b^{2}\sin^{2}x)^{2}}$

Find $\int_{0}^{\infty }\frac{\cos x-\cos x^2}{x}\mathrm dx$

What is cosine to the power of zero?