# Who's up to the challenge? 51

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, $$\displaystyle G = \sum_{n=0}^\infty \dfrac{ (-1)^n}{(2n+1)^2} \approx 0.916$$.

×