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Calculus Level 5

011+x13dx=abπcsc(πc) \large \displaystyle\int _{ 0 }^{ \infty }{ \dfrac { 1 }{ 1+{ x }^{ 13 } } \, dx } =\dfrac { a }{ b } \pi \csc { \left( \dfrac { \pi }{ c } \right) }

If the equation above holds true for positive integers a,ba,b and cc, with a,ba,b coprime, find a+b+ca+b+c.

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