Use the techniques I show at https://www.mathworks.com/matlabcentral/answers/890822-how-can-i-integrate-a-function-which-has-three-variables-but-has-to-integrate-it-with-respect-to-onl#answer_759472
syms s t d e real
y=((0.005659*s^2+0.05206*s+0.004496)/(s^3+9.357*s^2+2.228*s+0.06147))*((27.5084*d)+(27.5084*(e/s)))
z = ilaplace(y,s,t)
You are not going to get anywhere with symbolic integration until you convert the sum of root() into an expression without root() .
Even then you are not likely to get anywhere until you substitute in numeric d and e values.
