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In the probability theory,
selfdecomposable
or
class L
0
distributions
play an important role as they are limit distributions of normalized partial sums of sequences of independent, not necessarily identically distributed, random variables. The class
L
0
is quite large and includes many known classical distributions. For this note, the most important feature of the selfdecomposable variables are their random integral representation with respect to a Lévy process. From those random integral representations we get the equality of logarithms of some characteristic functions. These allow us to get formulas for some definite integrals; some of them were previously unknown, and some are rarely quoted in popular tables of integrals and series.