IVP Laplace Transform Problem -- Tricky Inverse Laplace Transform 1. The problem statement, all variables and given/known data Solve x"+x'+x=1, given x(0)=x'(0)=0 2. Relevant equations 3. The attempt at a solution Plugged in transforms: s2*Y(s)-s*y(0)-y'(0)+s*Y(s)-y(0)+Y(s)=1/s Plugged in initial value points, simplified to Y(s)=1/((s2+s+1)*s) Partial Fractions led me to Y(s)=1/s+ (-s-1)/(s^2+s+1) I get stuck at finding an inverse transform for the second term. You can't complete the square for the denominator, right?