  The logarithmic integral no. 4.325.7 from Gradshteyn and Ryzhik's tables of
integrals was first evaluated by Malmst\'en. Recently, Blagouchine used contour
integration methods to evaluate a family of logarithmic integrals that contains
this integral. We evaluate the integral in a simple, straightforward manner
mainly by means of real analysis. The main ingredients of the evaluation are
the use of geometric series and Kummer's Fourier series expansion for the
logarithm of the gamma function.
