Chapter 7.12, Problem 22P

The function $j_1(\alpha )=(\alpha \cos \alpha -\sin \alpha )/\alpha$ is of interest in quantum mechanics. [It is called a spherical Bessel function; see Chapter 12, equation (17.4).] Using problem 18, show that ${\displaystyle {\int }_0^{\infty }j}1(\alpha )\sin \alpha xd\alpha =$