According the ver 5.16.1 manual entry for ilt(...)
"Computes the inverse Laplace transform of expr with
respect to s and parameter t. expr must be a
ratio of polynomials whose denominator has
only linear and quadratic factors."
Here is an example where the denominator is
a cubic:
(%i1) display2d : false$
(%i2) fs : -s/(s^3 + 4*s^2 + 5*s +2)$
(%i3) ilt( fs, s, t );
(%o3) t*%e^-t - 2*%e^-t + 2*%e^-( 2*t )
(%i4) collectterms(%, exp(-t), exp(-2*t) );
(%o4) (t - 2)*%e^-t + 2*%e^-( 2*t )
Ted Woollett