Infinite Sums, Infinite Integrals

Calculus Level 4

\[\Large{\sum_{n=1}^\infty \dfrac{1}{n}\int_{\pi n}^\infty \dfrac{\sin(x)}{x} \, dx}=\dfrac{\pi}{a}\left(b-\ln\left(\dfrac{\pi}{c}\right)\right)\] \[\]If the equation above is true for integer constants \(a,b\) and \(c,\) find \(a+b+c.\)

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