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Comment #11 on issue 1304 by asmeurer: Integrate sqrt(x**2 + y**2) fails
http://code.google.com/p/sympy/issues/detail?id=1304
The way it is implemented, it needs to know the sign of z**2 (so it knows
whether to return an asinh or asin). The patch mentioned by comment 8 adds
a test of this, and it is +1 (I have pushed it in).
In [1]: z = Symbol('z', positive=True)
In [2]: integrate(sqrt(x**2 + z**2), x)
Out[2]:
2 ⎛x⎞ ⎽⎽⎽⎽⎽⎽⎽⎽⎽
z ⋅asinh⎜─⎟ ╱ 2 2
⎝z⎠ x⋅╲╱ x + z
─────────── + ──────────────
2 2
Ideally, this would return the result with the logarithm, but that would
require some more advanced algebraic integration machinery.
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