Sympy will not compute this integral

Question

I'm trying to run the following sample in sympy

import sympy as sp
from sympy.parsing.sympy_parser import parse_expr

n, L, x = sp.symbols('n L x')    
sp.integrate(sp.cos(sp.pi*x/L)**2, (x, -L/2, L/2))

For some reason, it does not actually solve this integral. It just prints out the original integral.

>>> sp.integrate(sp.cos(sp.pi*x/L)**2, (x, -L/2, L/2))
  L
  -
  2
  /
 |
 |     2/pi*x\
 |  cos |----| dx
 |      \ L  /
 |
/
-L
---
 2

Wolfram Alpha, on the other hand, does not have this issue.

Do not appreciate the sarcasm. Obviously this integral is computable, and SymPy is not doing it. Why is that the case? — ReckoningReckoner
There was no sarcasm. I can think of other questions you could be asking. You are more likely to get good answers here if you make your questions explicit and clear. It also helps to avoid criticizing the people trying to help you. You may want to delete your comment and add the relevant information to your main question. — Rory Daulton

saintsfan342000 saintsfan342000 · Accepted Answer · 2017-09-27T01:13:16

It seems a bit annoying, but sympy isn't evaluating the integral because it doesn't know enough about L. Specifically, it is leaving the door open to the possibility L=0, which would wreak havoc on your integrand. To overcome this we simply need to inform sympy that L is not zero. The easiest way to do this is to pass an argument to symbols during instantiation:

import sympy as sp
n, x = sp.symbols('n x')    
L = sp.symbols('L', nonzero=True)
sp.integrate(sp.cos(sp.pi*x/L)**2, (x, -L/2, L/2))
#>>> L/2

Sympy will not compute this integral

1 Answers