Who's up to the challenge? 50

Calculus Level 5

\[\large \int _{ 0 }^{ \infty }{ \frac { \ln { \sqrt [ 50 ]{ x } } }{ { e }^{ { x }^{ 2 }+1 } } dx } =-\dfrac { \sqrt { \pi } \left( a\gamma +\ln { b } \right) }{ ce } \]

If the above equation holds true for positive integers \(a,b\) and \(c\), find \(a+b+c\).

Notation: \( \gamma\) denotes the Euler-Mascheroni constant, \(\gamma \approx 0.5772 \).

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