Inspired by Hummus
Calculus
Level
5
\[ \int _{ 0 }^{ 1 }{ \left\{ \dfrac { 1 }{ { x }^{1/6 } } \right\} \,dx } =\dfrac { A }{ B } -\dfrac { { \pi }^{ C } }{ D } \]
The equation above holds true for positive integers \(A,B,C,\) and \(D\), with \(A\) and \(B\) coprime.
Find \(A+B+C+D\).
Notation: \( \{ \cdot \} \) denotes the fractional part function.
by
Aditya Kumar