Comment #5 on issue 1452 by asmeurer: integrate cannot do integral
http://code.google.com/p/sympy/issues/detail?id=1452
I can confirm it:
In [3]: integrate(1/(x*sqrt(1-x**2)),x)
Out[3]:
⎛ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ ⎞
⎛ 2⎞ ⎜ ╱ 2 ⎟
log⎝-x ⎠ ⎜╲╱ - x + 1 1⎟
──────── - log⎜───────────── + ─⎟
2 ⎝ 2 2⎠
How does it do it? Did you implement indefinite integration?
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