Created a pull request to fix the 
issue https://github.com/sympy/sympy/pull/12971

On Friday, July 7, 2017 at 11:11:24 AM UTC+3, Aaron Meurer wrote:
>
> 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] 
> <javascript:>> 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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