The Leibniz integral rule gives a formula for differentiation of a definite
integral whose limits are functions of the differential variable,
(1)
It is sometimes known as differentiation under the integral sign.
This rule can be used to evaluate certain unusual definite integrals such as
(2)
(3)
for
(Woods 1926).
Feynman (1997, pp. 69-72) recalled seeing the method in Woods (1926) and remarked "So because I was self-taught using that book, I had peculiar methods for doing integrals," and "I used that one damn tool again and again."
(Woods 1926).
