It seems this is a bug. I opened https://github.com/sympy/sympy/issues/12899.

Aaron Meurer

On Fri, Jul 7, 2017 at 4:05 AM, Fabrice Silva <[email protected]> wrote:
> Dear Sympiers,
> I have been puzzled by the results of the integration on some unknown
> function of several variables. For instance:
>
>>>> import sympy as sy
>>>> x, y, t = sy.symbols('x y t', real=True)
>>>> vx = sy.Function('v_x')(x,y,t)
>
> vx being thought as a scalar field in the 2D plane.
>
>>>> sy.integrate(vx, (y))
> gives the expected primitive of the field wrt the second argument y.
> However
>>>>sy.integrate(vx.diff(x), (y))
> assumes that vx.diff(x) does not depend on y, and thus the primitive is
> simply y*vx.diff(x).
>
> Did I miss some fundamental point in this trivial example ?
> Best regards
>
> Fabrice
>
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