$\displaystyle \large \int _{ 0 }^{ \pi /2 }{ \ln(\cos(x))\ln(\sin(x)) \ dx }$

The above integral can be expressed as

$\dfrac { \pi ( \ln B)^A }{ C } -\dfrac { { \pi }^{ D } }{ E }$

for positive integers $A,B,C,D,E$, with $B$ is not a perfect power of any integer, find $A+B+C+D+E$.