Comment #7 on issue 2219 by ronan.l...@gmail.com: Arbitrary constants in
indefinite integration
http://code.google.com/p/sympy/issues/detail?id=2219
I don't think 3) can currently be done in a way that's meaningful.
Consider the PDE d²f/dxdy = 0, we'd like the solution to be
integrate(integrate(0, y), x), but integrate(0, y) := C_1 and
integrate(C_1, x) := C_1*x + C_2 - which isn't at all the same thing as the
actual solution: h_1(x) + h_2(y).
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