Chapter 8.8, Problem 1P

For integral $k$, verify L5 and L6 in the Laplace transform table. Hint: From L2, you can write: ${\displaystyle {\int }_0^{\infty }{e}^{-pt}}{e}^{-at}dt=1/(p+a).$ Differentiate this equation repeatedly with respect to $p$.

(See Chapter 4, Section 12, Example 4, page 235.) Also note L32. For the $\Gamma$ function results in L5 and L6, see Chapter 11, Problem 5.7.