How to write and evaluate indefinite integrals (in Python, using SymPy)
Task
The antiderivative of a function is expressed using an indefinite integral, as in
\[\int f(x)\;dx.\]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 )
$\displaystyle 2 x^{\frac{3}{2}}$
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integrate( formula, x ) + var('C') # same, but with a constant of integration
$\displaystyle C + 2 x^{\frac{3}{2}}$
Content last modified on 24 July 2023.
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Contributed by Nathan Carter (ncarter@bentley.edu)