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Calculus Level 5

\[\int _{ 0 }^{ 1 }{ \dfrac { (1-{ x })\ln {(1- x) } }{ 1+{ x }^{ 2 } } \, dx } =-G+\dfrac { { a\pi }^{ b } }{ c }- \dfrac {(\ln f)^d} g +\dfrac { \pi \ln { h } }{ j } \]

The equation above holds true for positive integers \(a,b,c,d,f,g,h\) and \(j\), with \(a,c\) coprime and both \(f,h\) minimized.

Find the value of \(a+b+c+d+f+g+h+j\).

Notation: \(G\) denote Catalan's constant, \(\displaystyle G = \sum_{n=0}^\infty \dfrac{ (-1)^n}{(2n+1)^2} \approx 0.916 \).

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