# How do I evaluate int e^{6x} cos 5x dx?

Now you use a trick...taking the integral on the right to the left of the $=$ sign:
$\int {e}^{6 x} \cos \left(5 x\right) \mathrm{dx} = {e}^{6 x} / 61 \cdot \left[6 \cos \left(5 x\right) + 5 \sin \left(5 x\right)\right] + c$