16.1.1 Elaborating an example in SymPy

To begin with, let's elaborate on the previous example in SymPy and explain the steps.

First, we have to import the module:

from sympy import *
init_printing()

The second command makes sure that formulas are presented in a graphical way, if possible. Then, we generate a symbol and define the integrand:

x = symbols('x')
f = Lambda(x, 1/(x**2 + x + 1))

x is now a Python object of type Symbol and f is a SymPy Lambda function (note the command starting with a capital letter).

Now we start with the symbolic computation of the integral:

integrate(f(x),x)    

Depending on your working environment, the result is presented in different ways; see the following screenshot (Figure 16.2), which represents two different results of a SymPy formula in different environments:

We can check by differentiation...