When exponents meet trigonometry...

Calculus Level 3

The integration of e 3 x e^{3x} cos x with respect to x can be expressed as p q \frac{p}{q} e 3 x e^{3x} sin x + r s \frac{r}{s} e 3 x 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?


The answer is 24.

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