Inverse laplace with undefined variable
Here's a little help with the partial fraction decomposition: -
$$\dfrac{1}{s}\cdot \dfrac{k}{s^2 + s +k}\hspace{1cm} =\hspace{1cm} \dfrac{1}{s}+ \dfrac{-s-1}{s^2 + s + k}$$
Can you take it from here?
If not try this inverse laplace solver.