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Finding $\int_{1}^{\infty} \frac{1}{1+x^2} \frac{\operatorname{Li}_2\left ( \frac{1-x}{2} \right ) }{\pi^2+\ln^2\left(\frac{x-1}{2}\right)}\text{d}x$
Prove the integral
$$\int_{1}^{\infty} \frac{1}{1+x^2}
\frac{\operatorname{Li}_2\left ( \frac{1-x}{2} \right ) }{
\pi^2+\ln^2\left ( \frac{x-1}{2} \right ) }\text{d}x
=\frac{96C\ln2+7\pi^3}{12(\pi^2+...
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Compute this following integral without Fourier series : $\int_0^{\pi/4}x\ln(\tan x)dx$
Compute the following integration without harmonic series or Fourier series :
$I=\displaystyle\int_0^{\frac{π}{4}}x\ln(\tan x)dx$
Wolfram alpha give $I=\frac{7\zeta(3)-4πC}{16}$
Where $C$ : Catalan'...
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