Feynman Trick to differentiate under integral sign

In his autobiographical vignettes book “Surely you’re joking”…, he only really mentions several times that he solved problems that had stumped other scientists for weeks or months because apparently this technique did not get commonly used. As he described it, it was just one of his last line tools for hard integrals and he would ask stumped people if they tried it and they often said no. I think he even mentioned learning it out of a high school calculus book, but it was never covered in class.

It just wound up in his amusing self-image promoting stories, but his factual claims regarding it seem honest enough.