Who's up to the challenge? 31

Calculus Level 5

01{1x17291(1x)1729}x6(1x)6dx=ab \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 aa and bb. Find a+ba+b.

Bonus: Generalize it.

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


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