The modern proof is to use an antiderivative: the derivative of xn is shown to be nxn−1 – for non-negative integers. This is shown from the binomial formula and the definition of the derivative – and thus by the fundamental theorem of calculus the antiderivative is the integral. This method fails for ∫ 1 x d x , {\displaystyle \int {\frac {1}{x}}\,dx,} as the candidate antiderivative is 1 0 ⋅ x 0 {\displaystyle {\frac {1}{0}}\cdot x^{0}} , which is undefined due to division by zero.