Updates:
Blockedon: -sympy:2010
Comment #3 on issue 2277 by asmeu...@gmail.com: integrate(3 + exp(1/x**2),
x) doesn't return successful parts.
http://code.google.com/p/sympy/issues/detail?id=2277
This is a bad example, because this actually does have an answer
In [17]: integrate(3 + exp(1/x**2), x)
Out[17]:
1
──
2
x ___ ⎛ⅈ⎞
x⋅ℯ + 3⋅x + ⅈ⋅╲╱ π ⋅erf⎜─⎟
⎝x⎠
In [18]: integrate(3 + exp(1/x**2), x).diff(x)
Out[18]:
1
──
2
x
ℯ + 3
Anyway, Risch's ability to pull out integrals is rather limited. For
example:
In [26]: integrate(3 + x**x, x)
Out[26]:
⌠
⎮ ⎛ x ⎞
⎮ ⎝x + 3⎠ dx
⌡
but
In [33]: integrate(exp(x) + 1/log(x), x, risch=True)
Out[33]:
⌠
x ⎮ 1
ℯ + ⎮ ────── dx
⎮ log(x)
⌡
Basically, it only works if it happens to compute some part of the integral
before it finds the rest to be nonelementary, which is relatively rare
(even in this second case, it only happens because it happens to integrate
with respect to the exponential before the logarithm).
So there is still a lot of work that can be done here.
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