Who's up to the challenge? 19

Calculus Level 5

$\large \int_0^1 ( \ln x)^3 \ln (1-x^2) \, dx$

The value the integral above is equal to

$-\dfrac { A }{ B } \zeta (C)-\dfrac { D }{ F } { \pi }^{ G }+H-\dfrac { \pi ^{ J } }{ K } -L\ln { 2 },$

where $$A,B,C,D,F,G,H,J,K$$ and $$L$$ are positive integers with $$\gcd(A,B) = \gcd(D,F) = 1$$.

Find $$A+B+C+D+F+G+H+J+K+L$$.

this is a part of Who's up to the challenge?

×