What mathematical technique for solving integrals did Feynman popularize?

The mathematical technique Richard Feynman popularized for solving integrals was differentiation under the integral sign. It is also widely called “Feynman’s trick.”

The method introduces a parameter into an integral, differentiates the resulting expression with respect to that parameter, evaluates the usually simpler integral, and then integrates back. This can transform a difficult integral into a manageable differential-equation problem. The underlying result is a form of the Leibniz integral rule, so Feynman did not invent the general mathematical principle.

Feynman encountered the technique in Frederick S. Woods’s Advanced Calculus while he was still in high school. He later recalled using it repeatedly when standard techniques failed, including during his studies at MIT and Princeton. His memoir helped make the method famous among students and physicists. A common mix-up is to treat it as a distinct integration formula invented by Feynman; more precisely, he became its celebrated advocate and demonstrated its practical power in solving otherwise stubborn definite integrals.