William Stein wrote:

> Unless you can give a explanation of what you want integrating wrt x^2
> to mean, I think we should also raise an error in Sage.

That would be unfortunate. Faced with some unrecognized construct,
the mathematical thing to do is to just leave it be. Whether it's
meaningful is for the user to decide. You don't know what
integrate(f(x), g(x)) means. Why not let someone else come
up with an interpretation? Why must you close that door?

Incidentally, integrate(f(x), g(x)) = integrate(f(g^(-1)(y)), y), when
g^(-1) is well defined, seems plausible. I'm not saying Sage should
apply such an identity, only that Sage should not prevent the user
from applying it.

I agree that Maxima's result for integrate(f(x), x^2) is spurious.

FWIW

Robert Dodier
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