integral calculator in R

I know how to use integral calculator to obtain numeric values, but don't know how to get an algebraic equation.

For example:

integrand <- function(x) {1/((x+1)*sqrt(x))} integrate(integrand, lower = 0, upper = Inf) 

with this code, I can get 3.141593 with absolute error < 2.7e-05

However, what if I want to use this code:

integrand <- function(x) {2*x} integrate(integrand, lower = -Inf, upper = Inf) 

to get x^2.

Apparently, it does not work.

If someone can help this, I would appreciate your help. Tons of thanks!

1 Answer

R doesn't do symbolic math but there are R packages that do. I will give (very) short examples using CRAN packages Ryacas and rSympy.

1. Package Ryacas.

library(Ryacas) f <- ysym("2*x") integrate(f, "x") #y: x^2 

2. Package rSymPy.

With package rSymPy you need to define the symbol "x" first. This is done with function Var.
Note: in my tests, the first time any of Var or sympy were called a series of warnings were given. I have interrupted R and at the second time all went well.

library(rSymPy) x <- Var("x") sympy("integrate(2*x)") #[1] "x**2"