Seems Complex

Calculus Level 5

$\large \int_ {-\infty}^{\infty}{\frac{\cos{(3x)}}{ {({x}^{2}+25)}^{2} }} \, dx$

If the value of the above integral is equals to $$\large \frac{a\pi}{b {e}^{c}}$$ where $$e$$ is Euler's number and $$a,b$$ are coprime positive integers, what is the value of $$a+b+c$$?

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