Integral of inverse functions

In mathematics, integrals of inverse functions can be computed by means of a formula that expresses the antiderivatives of the inverse f − 1 {\displaystyle f^{-1}} of a continuous and invertible function f {\displaystyle f} , in terms of f − 1 {\displaystyle f^{-1}} and an antiderivative of f {\displaystyle f} . This formula was published in 1905 by Charles-Ange Laisant.