Use integration by parts to show that $$\[ \int \mathrm{e}^{2 x} \cos 3 x \mathrm{~d} x=p \mathrm{e}^{2 x} \sin 3 x+q \mathrm{e}^{2 x} \cos 3 x+k \]$$ where $$\(p\)$$ and $$\(q\)$$ are rational numbers to be found and $$\(k\)$$ is an arbitrary constant. (6)

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