# Indefinite integral

This article/section deals with mathematical concepts appropriate for a student in late high school or early university. |

An **indefinite integral**, or antiderivative, is an integral without upper and lower limits.

## Contents

## Indefinite Integrals

There are an infinite number of antiderivatives for a given function, because each indefinite integral can have an arbitrary constant added to it which disappears upon differentiation. However, the fundamental theorem of calculus relates a definite integral to an indefinite integral by taking its value at the boundary points.

Whenever any expression is integrated the constant of integration, , is always added.

## A list of simple antiderivatives

The identity antiderivative:

### Polynomial and simple rational

To see the proofs for the first two integrals, see Riemann integral.

The general rule for polynomial expressions is:

Note: . See below for when

### Rational

*For a more detailed treatment, see Partial fractions in integration.*

Rational antiderivatives are much more difficult and follow different rules.