CODEWITHSUNDEEP
pythonexpressionsympysymbolic-integration
João Pedro Farineli
João Pedro Farineli

Reputation: 11

How to integrate expressions with sympy?

I have a problem integrating an expression:

I need to integrate all terms regardless of the variable,

the expression: -x + 2 * (x - 1)

Expected result: -x**2/2 + 2 * ((x - 1)**2) / 2

the code I'm using:

from sympy import *

x = symbols('x')

expr = - x + factor(2 * (x - 1))
int_1 = integrate(expr)
print(int_1)

generated result: x**2/2 - 2*x

Upvotes: 1

Views: 208

Answers (2)

smichr
smichr

Reputation: 18979

If you check your result you will find it is the same as the original equation, so the answer is right:

>>> eq = -x + factor(2 * (x - 1))
>>> integrate(eq).diff()
x - 2
>>> eq.expand()
x - 2

This means that the result you got differed from the expected results by a constant and such cases are considered correct in terms of indefinite integration.

It looks like you already learned about autoexpansion (thus the use of factor to keep the 2 from distributing). What you may not realize, however, is that once you pass an expression to a routine it is not required to keep your expression in factored form. It looks like you were expecting that the x - 1 would be treated like x. We can simulate that as

>>> integrate(-x)+integrate(2*y).subs(y,x-1)
-x**2/2 + (x - 1)**2

Using y to represent x - 1 is ok in this case since the results only differ by a constant:

>>> (integrate(x-1) - integrate(y).subs(y ,x-1)).is_constant()
True

It will not, however, be true for all functions of x.

Upvotes: 2

Jano
Jano

Reputation: 455

The problem is that you didn't pass any integration limits (from and to), so the only possible answer was the integrated formula.

If for example you want to integrate from 0 to inf, you need to pass this instead

from sympy import *

x = symbols('x')

expr = - x + factor(2 * (x - 1))
int_1 = integrate(expr, (x,0, float('inf')))
print(int_1)

replace 0 and/or float('inf') by any numbers you want to evaluate.

Upvotes: -1

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