Why does x(x+y) dy give a x^3 component?

syms g(x,y) x y
g(x,y) = 2*x+y;
gx = int(g, x);
int(gx, y)

The function gx becomes x*(x+y), so far so good. But int(gx, y) returns:

(x*(x + y)^2)/2

- which has a x^3 component in x*(x+y)^2. How could this happen?

doc int 

The documentation refers me to the sym page, which does not mention "int" or "diff". Integration works fine for g(x,y)=y, but I've not tested much else.

Thanks.

[darova]

I want to know it too

[Bob Thompson]

It seems to be an issue with factoring. If you expand gx into x^2 + x*y and conduct the integration you get (x*y*(2*x + y))/2, which my fading memory of integration says is correct.

Answer 1

[Koushik Vemula]

Both answers are correct.

d/dy[ x*(x+y)^2/2 ] = d/dy[ (x^3)/2 + x^2*y + y^2*x/2 ] = x*(x + y)

d/dy[ x*y*(2*x+y))/2 ] = x*(x + y)

The ambiguity lies in the constant of integration. In the first case the constant of integration ends up being (x^3)/2.

If you really want to enforce that the constant of integration is zero then do:

int(gx,y,0,y) 

In other words

int(x*(x+y),y,0,y) 

[darova]

Thank you