Status: Accepted
Owner: ----
Labels: Type-Defect Priority-Medium Assumptions Integration WrongResult

New issue 2808 by [email protected]: integrate(1/(x**2 + a**2)**2, x) is wrong if a is real
http://code.google.com/p/sympy/issues/detail?id=2808

In [4]: a = Symbol('a', positive=True)

In [5]: integrate(1/(x**2 + a**2)**2, x)
Out[5]:
                     ⎛x⎞
                 atan⎜─⎟
      x              ⎝a⎠
────────────── + ───────
   4      2  2        3
2⋅a  + 2⋅a ⋅x      2⋅a

In [6]: a = Symbol('a', real=True)

In [7]: integrate(1/(x**2 + a**2)**2, x)
Out[7]:
      x
──────────────
   4      2  2
2⋅a  + 2⋅a ⋅x

It's easy to check that the first result is correct and the second is not.

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