Formal integral ($I\left({\sum }_{n\ge 0}{a}_n{x}^n\right)={\sum }_{n\ge 0}\frac{a_n}{n+1}{x}^{n+1}$)

For a formal power series over a field of characteristic zero, the displayed coefficientwise operation chooses constant coefficient zero. Its formal derivative is the original formal power series: differentiating the term with exponent $n+1$ cancels its denominator. Conversely, formally integrating a formal derivative removes the original constant term. These are algebraic identities; analytic convergence is not required.