# 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.

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