Let
denote our integral. Then, evidently
Switch the order of integration (Fubini's theorem is satisfied) to get
Rewrite this as
Make the obvious substitution (
) on the inside to turn it into
Thus, the first integral being easy, and the second being the definition of the
Euler-Mascheroni constant we find that
To prove the second assertion merely write the exponentials in complex notation and separate the real and imaginary parts. The theorem then becomes immediate from the common theorem that