Fractional Party! 1

Calculus Level 5

0101{xy}3{yx}3dx  dy=AπBCπB+2Dζ(E)\large \int_0^1 \int _{ 0 }^{ 1 }{ { \left\{ \dfrac { x }{ y } \right\} }^{ 3 }{ \left\{ \dfrac { y }{ x } \right\} }^{ 3 } \, dx \; dy } =A-\dfrac { { \pi }^{ B } }{ C } -\dfrac { { \pi }^{ B+2 } }{ D } -\zeta \left( E \right)

The equation above holds true for positive integers A,B,C,DA,B,C,D and EE. Find A+B+C+D+EA+B+C+D+E.

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