Trouble with integral of ln(x-y)

[Filip]

I'm trying to calculate the integral of ln(x-y) dy (with x and y complex)

>> integrate(ln(x-y), y)

but sympy gives me 

    -x*log(-x + y) + y*log(x - y) - y

If I try to differentiate this wrt. y I get

>> diff(-x*log(-x + y) + y*log(x - y) - y, y)

    -x/(-x + y) - y/(x - y) + log(x - y) - 1

which is not exactly equal to ln(x-y).

As far as I know the result of the integration should be -ln(x - y)*(x - y) + x - y, which also gives the correct result when differentiated in sympy

>> diff(-ln(x-y)*(x-y)+x-y, y)

    log(x - y)

The calculations can be seen as a IPython Notebook here

http://nbviewer.ipython.org/gist/FSund/2a49222b54fa95ccdbc0

[Aaron Meurer]

On Thu, Oct 22, 2015 at 2:45 AM, Filip <filip...@gmail.com> wrote:
> I'm trying to calculate the integral of ln(x-y) dy (with x and y complex)
>>> integrate(ln(x-y), y)
> but sympy gives me
> -x*log(-x + y) + y*log(x - y) - y
> If I try to differentiate this wrt. y I get
>>> diff(-x*log(-x + y) + y*log(x - y) - y, y)
> -x/(-x + y) - y/(x - y) + log(x - y) - 1

If you call simplify() on this you get log(x - y)

> which is not exactly equal to ln(x-y).
> As far as I know the result of the integration should be -ln(x - y)*(x - y)
> + x - y, which also gives the correct result when differentiated in sympy

Remember that integrals can differ by a constant. In this case, the
argument of one of the logs is negated from what you expect, but this
amounts to a complex constant.

Aaron Meurer

>>> diff(-ln(x-y)*(x-y)+x-y, y)
> log(x - y)
>
> The calculations can be seen as a IPython Notebook here
> http://nbviewer.ipython.org/gist/FSund/2a49222b54fa95ccdbc0
>

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