# Who's up to the challenge? 31

Calculus Level 5

$\large \displaystyle\int _{ 0 }^{ 1 }{ \left\{ \dfrac { 1 }{ { x }^{ 1729 } } -\dfrac { 1 }{ (1-x)^{ 1729 } } \right\} { x }^{ 6 }(1-x)^{ 6 } \, dx } =\dfrac { a}{ b }$

The equation above holds true for coprime positive integers $$a$$ and $$b$$. Find $$a+b$$.

Bonus: Generalize it.

Notation: $$\{ \cdot \}$$ denotes the fractional part function.

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