# Summation Contest Conceptual Problem-2

**Calculus**Level 5

\[\int _{ 0 }^{ 1 }{ \dfrac { x{ ( 1-x ) }^{ 1/4} }{ { \left( 2-x \right) }^{ 2 } } dx } =-A+\frac { B\pi \sqrt { C } }{ D } +\frac { E\sqrt { F } \ln { ( 1+\sqrt { G } ) } }{ H } \]

The above equation is true for positive integers \(A\), \(B\), \(C\), \(D\), \(E\), \(F\), \(G\) and \(H\). Find the minimum value of \(A+B+C+D+E+F+G+H\).

**Hint:** Use partial fractions after making a good substitution.