Updates:
        Blockedon: 1336

Comment #8 on issue 2219 by asmeurer: Arbitrary constants in indefinite integration
http://code.google.com/p/sympy/issues/detail?id=2219

That's because integrate(0, y) == C_1(x), not C_1.

What is really needed is some way to say what the constants are constants with respect to (instead of the reverse). And then it would be assumed that they are not constant with respect to anything else in general. I seem to remember suggesting this somewhere in the past, but I don't know where it is by now.

But I agree that barring this kind of advanced functionality, which would almost have to have a special object a la issue 1336, integrate(constant=True) should just return a C (or C_n) term, and not a function.

Also, I want to point out that in general, if you want to get arbitrary constants, you should pass your function to dsolve() or pdesolve(). dsolve() at least can handle any ode of the form f(x).diff(x, n) = g(x) via variation of parameters method, or even the very fast constant coefficients method if g(x) has the right form. Of course, this requires converting the integral into an ode/pde, which I think might be non-trivial at least in the pde case.

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