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Calculus Level 5

\[\large \int _{ -\infty }^{ \infty }{ \dfrac { \ln { (1+{ e }^{ 2x } } ) }{ 1+{ e }^{ 3x } } \, dx } =\frac { A\pi ^{ C } }{ B } \]

If the equation above holds for coprime positive integers \(A,B\) and an integer \(C\), then find \(A+B+C\).

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