# Log with Dilog

Calculus Level 5

$\int_0^1 {\rm Li}_2 \left(\dfrac{x}{2}\right)\log(1-x)\; dx = A+\dfrac{\log^B C}{D}+\dfrac{\zeta(E)\log F}{G}-\zeta(H)-\zeta(I)-J\log(K)$

If the above equation holds true for positive integers $$A,B,C,D,E,F,G,H,I,J,K$$ not necessarily distinct then find $$A+B+C+D+E+F+G+H+I+J+K$$.

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