Solution
= Solution
For a function for which the integral converges, the <Laplace transform> is
$$
\bar f(p)=\int_0^\infty e^{-pt}f(t)\,dt.
$$
For a <continuous> function of <exponential order> this exists in a sufficiently far right half-plane. For the first input,
$$
\boxed{\overline1(p)=\frac1p\qquad(\operatorname{Re}p>0).}
$$
This follows by evaluating the exponential antiderivative and using its decay at infinity.