Because has an infinite discontinuity at it might be assumed that does not exist;

Chapter 7, Problem 67

(choose chapter or problem)

Because has an infinite discontinuity at it might be assumed that does not exist; however, this is incorrect. The point of this problem to guide you through the formal steps leading to the Laplace transform of (a) Use integration by parts to show that (b) If , use Theorem 7.4.1 with to show that part (a) becomes Find an explicit solution of the foregoing differential equation. (c) Finally, the integral definition of Eulers constant (sometimes called the Euler-Mascheroni constant) is , where . . . . Use in the solution in part (b) to show that