1.) Isn't perform Laplace/inverse as in red circle against the rule ? (it is multiplication of two term, we cannot take it separately)

2.) how come sign change from - to +

Now apply inverse Laplace transform L1{X(s)}=L1{s1}L1{e2s[s1s2+1s]}L1{X(s)}=1+a(t2)[1cos(t)] Thus, x(t)={1costt