In calculus, integration by substitution — popularly called u-substituion or simply the substitution method — is a technique of integration whereby a complicated looking integrand is rewritten into a simpler form by using a change of variables: , where . In the case of a definite integral, , where , . Integration by u-substitution is the inverse operation of the chain rule from differential calculus. It is also the two-dimensional version of using a Jacobian matrix to transform coordinates.