Why is my Laplace Inverse wrong?

[corolla]

I am doing Laplace inverse here and get the following answer, but when I check online, it shows a much more elaborate answer that I don't understand. Why is my answer wrong? What steps do I take to get the correct answer?

E-math help answer:

Symolab answer:

 

[stapel]

Can you distribute like that?

 

[BobP]

[imath]L^{-1}\{e^{-as}F(s)\}=u(t-a)f(t-a), \text{ where }L^{-1}\{F(s)\}=f(t).[/imath]

In order to calculate [imath]f(t)[/imath] you have to split [imath]1/\{(s^{2}+4)(s+1)s\}[/imath] into the partial fractions

[imath](As+B)/(s^{2}+4)+C/(s+1)+D/s.[/imath]