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∫01{1x1/6} dx=AB−πCD \int _{ 0 }^{ 1 }{ \left\{ \dfrac { 1 }{ { x }^{1/6 } } \right\} \,dx } =\dfrac { A }{ B } -\dfrac { { \pi }^{ C } }{ D } ∫01{x1/61}dx=BA−DπC
The equation above holds true for positive integers A,B,C,A,B,C,A,B,C, and DDD, with AAA and BBB coprime.
Find A+B+C+DA+B+C+DA+B+C+D.
Notation: {⋅} \{ \cdot \} {⋅} denotes the fractional part function.
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