Patch here: http://plaes.org/files/2009-Q1/sympy-fix-asin-integral.patch
Previously sympy failed to integrate things like this:
In [3]: integrate(1/sqrt(9 + 4*x**2), x)
Out[3]:
⌠
⎮ 1
⎮ ───────────── dx
⎮ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽
⎮ ╱ 2
⎮ ╲╱ 9 + 4⋅x
⌡
With patch applied:
In [1]: integrate(1/sqrt(9 + 4*x**2), x)
Out[1]:
⎛2⋅x⎞
asinh⎜───⎟
⎝ 3 ⎠
──────────
2
This also uncovered a bug: just try to do this: integrate(1/sqrt(16 +
4*x**2), x)
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