Yes, see issue 2150. This has been fixed in my integration3 branch:
In [2]: integrate(1/(x**2 + a**2), x)
Out[2]:
⎽⎽⎽⎽ ⎛ ⎽⎽⎽⎽⎞ ⎽⎽⎽⎽ ⎛ ⎽⎽⎽⎽⎞
╱ -1 ⎜ 2 ╱ -1 ⎟ ╱ -1 ⎜ 2 ╱ -1 ⎟
╱ ── ⋅log⎜x + a ⋅ ╱ ── ⎟ ╱ ── ⋅log⎜x - a ⋅ ╱ ── ⎟
╱ 2 ⎜ ╱ 2 ⎟ ╱ 2 ⎜ ╱ 2 ⎟
╲╱ a ⎝ ╲╱ a ⎠ ╲╱ a ⎝ ╲╱ a ⎠
─────────────────────────────── - ───────────────────────────────
2 2
Unfortunately, this fix did not make it to my integration3-backport branch, but
I think I will bisect the code and see if I can cherry-pick the correcting
commit, since this is a wrong result.
Aaron Meurer
On Mar 26, 2011, at 6:41 PM, Yuri Karadzhov wrote:
> Do you know about this bug?
>
> a=Symbol('a')
>
> In [47]: integrate(1/(x**2+a**2))
> Out[47]: 0
>
> In [48]: integrate(1/(x**2+a**2),x)
> Out[48]: 0
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