I tried to calculate the indefinite integral of 1/(L-x)dx in sympy:
from sympy import *
x, L = symbols('x L')
f = 1/(L-x)
integrate(f, x)
it returned:
-log(-L + x)
while it should be:
-log(L-x)
Is it related to sympy or I missed something, thanks for any explanation.
I have not found an answer for this paricular function.
On
Can't tell you why that happens right now.
However, this is a simple function to integrate, so we can asks sympy to mimic integration by hands with the option manual=True:
f.integrate(x, manual=True)
# out: -log(L-x)
which is the result you are expecting.
On
Indefinite integrals are defined only up to an additive constant. The difference between log(x - L) and log(L - x) is I*pi which is a constant.
Considering that you might only be interested in real-valued expressions you might prefer one or the other form but which one integrate should return in that case is still ambiguous: the two expressions differ in that one gives real values for x > L and the other gives real values for x < L.
If you differentiate both with respect to
x, you'll find the same result. You can check with Wolframalpha.https://www.wolframalpha.com/calculators/derivative-calculator
As far as I understand you haven't provided constraints on L, so it can be positive or negative which I assume is the origin of your confusion. Regardless both formulae yield what you want.