Infinite derivative's series expansion of Indefinite and Definite Integral

TL;DR

This paper proves that indefinite integrals can be represented as infinite series of derivatives, providing a novel approach that also facilitates new methods for evaluating definite integrals.

Contribution

It introduces a new series expansion method for indefinite integrals using infinite derivatives, offering a fresh perspective on integral computation.

Findings

Indefinite integrals can be expressed as infinite derivative series.

The series expansion approach enables new techniques for definite integrals.

The existence of such series expansions is formally proven.

Abstract

In this article it is proven the existence of integration of indefinite integrals as infinite derivative's series expansion. This also opens a new way to integrate a definite integral.