When exponents meet trigonometry...

Calculus Level 3

The integration of \(e^{3x} \) cos x with respect to x can be expressed as \(\frac{p}{q}\) \(e^{3x} \) sin x + \(\frac{r}{s} \) \(e^{3x} \) cos x + c where c is the arbitrary constant. Assuming gcd (p, q) = 1 and gcd (r, s) = 1, what is p+q+r+s?

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