Inverse Laplace of a transfer function for $\frac{K_{s}.P_{0}}{s.(s.T_{1}+1)} + \frac{V_{a}}{s}$

Question

I have the following function in the Laplace domain: $$\frac{K_{s}.P_{0}}{s.(s.T_{1}+1)} + \frac{V_{a}}{s}$$

And I want to do the inverse Laplace transform.So, this is my result: $$L^{-1} (V(s))=K_s.P_0.(1- e^{(-t/T_1)})+ v_a$$

Could anyone check the correctness of my work?

Answer 1

Your answer looks correct. You can check that using WA. We need only use partial fraction decomposition and $\mathcal{L}[t^n] = \frac{n!}{s^{n+1}}$. Let me know if I can help.