Comment #7 on issue 2010 by asmeurer: Integration with the full Risch
Algorithm
http://code.google.com/p/sympy/issues/detail?id=2010
Well, I must have fixed that somewhere, because I get:
In [11]: integrate(1/((a-x)*(b-x)), x)
Out[11]:
⎛
⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽
⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽
⎞ ⎛
⎜ 2 ╱ 1 2
╱ 1
⎟ ⎜ 2 ╱
⎜ a ⋅ ╱ ──────────────── b ⋅
╱ ────────────────
⎟ ⎜ a ⋅ ╱
⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ ⎜ ╱ 2 2
╱ 2 2 ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎟
⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ ⎜ ╱
╱ 1 ⎜ a b ╲╱ -2⋅a⋅b + a + b
╲╱ -2⋅a⋅b + a + b ╱ 1 ⎟ ╱
1 ⎜ a b ╲╱
╱ ──────────────── ⋅log⎜x - ─ - ─ - ────────────────────────── -
────────────────────────── + a⋅b⋅ ╱ ──────────────── ⎟ - ╱
──────────────── ⋅log⎜x - ─ - ─ + ────────
╱ 2 2 ⎜ 2 2
2 2 ╱ 2 2
⎟ ╱ 2 2 ⎜ 2 2
╲╱ -2⋅a⋅b + a + b
⎝
╲╱ -2⋅a⋅b + a + b ⎠ ╲╱ -2⋅a⋅b + a + b ⎝
⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽
⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ ⎞
1 2 ╱
1 ⎟
──────────────── b ⋅ ╱
──────────────── ⎟
2 2 ╱ 2 2
⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎟
-2⋅a⋅b + a + b ╲╱ -2⋅a⋅b + a + b ╱
1 ⎟
────────────────── + ────────────────────────── - a⋅b⋅ ╱
──────────────── ⎟
2 2 ╱ 2
2 ⎟
╲╱ -2⋅a⋅b + a +
b ⎠
in my integration3 branch that is merged with polys11.
I haven't bisected yet, but I am guessing it is the fix from issue 1793
(add a composite option to Poly). We should still debug the code to see if
that really fixed the problem, or just masked it.
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