integrate in sympy

[Andreas Söll]

What am I doing wrong?

>>> from sympy import *       # Version 1.13.2
>>> x = symbols("x")
>>> f = x / (x+1)
>>> f
x/(x + 1)
>>> integrate(diff(f,x),x)    # should be x/(x+1)
-1/(x + 1)

diff seems correct - what about integrate?

Can anyone help?

[Oscar Benjamin]

Antiderivatives are not unique.

Generally
diff(integrate(f(x), x), x) == f(x)
but we don't necessarily have
integrate(diff(f(x), x), x) == f(x)
because they can differ by a constant of integration:

>>> cancel(f - integrate(diff(f, x), x))
1
>>> cancel(f - diff(integrate(f, x), x))
0

--
Oscar

[Andreas Söll]

Thank you very much for your quick help.
At first I was hesitant and tried a few things.
Your answer has now convinced me.

Best regards, Andreas

[Donaldson Tan]

 integrate(diff(f,x),x) actually yields you -1/(x + 1) + constant C

when u set C = 1, it becomes x/(x + 1)