We're on symbolic integration techniques in my Calc II class right
now, and SAGE rather nicely deals with many (but not all) of the
standard examples, or makes the usual mistakes various other systems
make (e.g., integrate(1/x) gives ln(x), not ln(abs(x))).

However, I'm stumped as to where this one comes from:

integrate(1/sqrt(9+x^2))
x/3

I tried this at home and numerous times on sagenb.org.  Every other
plausible syntax of this integral I tried (-1 power, more parentheses,
switch the summands, etc.) yields the same result.  Yet
surprisingly ;) I get

derivative(x/3)
1/3

Any ideas?


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