# integral.rationalfun: Integrate a rational function In rationalfun: Manipulation of Rational Functions

 integral.rationalfun R Documentation

## Integrate a rational function

### Description

Calculate the integral of a rational function. See "Details".

### Usage

```## S3 method for class 'rationalfun'
integral(expr, ...)
```

### Arguments

 `expr` an object of class "rationalfun" `...` not used in this function

### Details

The returned value is a function call with argument named "x". That is, the integral is an expression in R with an explicit form, which could be evaluated directly by calling `eval()`, or indirectly using the `int2fun()` function.

The algorithm is based on the Hermite-Ostrogradski formula which is discussed in the reference. See the article for more details.

### Value

A function call representing the explicit form of the integral.

### References

T. N. Subramaniam, and Donald E. G. Malm, How to Integrate Rational Functions, The American Mathematical Monthly, Vol. 99, No.8 (1992), 762-772.

`integral.polynomial`

### Examples

```# (x + 1) / (x^2 + x + 1)
r <- rationalfun(c(1, 1), c(1, 1, 1))
expr <- integral(r)
# Evaluate the call directly
eval(expr, list(x = 2))
# Use int2fun()
f <- int2fun(expr)
f(2)
```

rationalfun documentation built on March 18, 2022, 6:07 p.m.