Frullani integral

Frullani integrals are definite integrals of the form

where is a function over , and the limit of exists at

The following formula for their general solution holds under certain conditions:


This can be proved using the method of differentiation under the integral sign when the integral exists and is continuous.


  • G. Boros, V. Moll, Irresistible Integrals (2004), pp. 98
  • Juan Arias-de-Reyna, On the Theorem of Frullani (PDF; 884 kB), Proc. A.M.S. 109 (1990), 165-175.