I had a test yesterday and couldn't figure out the answer to this question. Was wondering if someone could walk me through the solution. $\dfrac{(13s+3)}{(s^2+2s+5)}$
I figured I had to complete the square in the denominator then split the fraction up into $\dfrac{13s}{(s+1)^2+4} + \dfrac3{(s+1)^2+4}$
That would allow me to solve the second fraction as $3/2 \exp(-t) \sin(2t)$.
I couldn't figure how to solve for the first fraction unless I shouldn't have split them up at all.
So what is the proper way to solve it?