How to write and evaluate indefinite integrals (in Python, using SymPy)

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Task

The antiderivative of a function is expressed using an indefinite integral, as in

How can we write and evaluate indefinite integrals using software?

Related tasks:

• How to compute the derivative of a function
• How to write and evaluate definite integrals
• How to write and evaluate Riemann sums

Solution

This answer assumes you have imported SymPy as follows.

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from sympy import *                   # load all math functions
init_printing( use_latex='mathjax' )  # use pretty math output

Let’s choose an example formula whose antiderivative we will compute.

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var( 'x' )
formula = 3*sqrt(x)
formula

${\displaystyle 3\sqrt{x}}$

Use the Integral function to build a definite integral without evaluating it. The second parameter is the variable with respect to which you’re integrating.

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Integral( formula, x )

${\displaystyle \int 3\sqrt{x}dx}$

Use the integrate function to perform the integration, showing the answer.

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integrate( formula, x )

${\displaystyle 2x^{\frac{3}{2}}}$

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integrate( formula, x ) + var('C')  # same, but with a constant of integration

${\displaystyle C+2x^{\frac{3}{2}}}$

Content last modified on 24 July 2023.

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Contributed by Nathan Carter (ncarter@bentley.edu)