Solution
= Solution
Combining the exponential factors gives
$$
\boxed{\overline{e^{-ct}}(p)=\int_0^\infty e^{-(p+c)t}\,dt=\frac1{p+c}\qquad(\operatorname{Re}(p+c)>0).}
$$
= Solution
Combining the exponential factors gives
$$
\boxed{\overline{e^{-ct}}(p)=\int_0^\infty e^{-(p+c)t}\,dt=\frac1{p+c}\qquad(\operatorname{Re}(p+c)>0).}
$$