10.4.29 Laplace transform

condition: Find (continuous on \( [0 ;+\infty)) \) the original function if its image \( F(p) \) is equal to: 1) \( F(p)=\frac{e^{-2 p}}{p+1} \), 2) \( F(p)=\left(e^{-2 p}+3 e^{-p}\right) \frac{1}{p} \)