Updates:
Labels: NeedsReview asmeurer
Comment #9 on issue 1892 by asmeurer: integrate(1/(x*(a+b*x)**3), x) fails
http://code.google.com/p/sympy/issues/detail?id=1892
My patch from issue 1793 unfortunately makes the output of this a little
more complicated, but it is still correct:
In [18]: integrate(1/(x*(a+b*x)**3), x)
Out[18]:
⎛
⎽⎽⎽⎽⎞ ⎛ ⎽⎽⎽⎽⎞
⎜ 4 ╱ 1
⎟ ⎜ 4 ╱ 1 ⎟
⎜ a - a ⋅ ╱ ──
⎟ ⎜ a + a ⋅ ╱ ── ⎟
⎽⎽⎽⎽ ⎜ ╱ 6 ⎟
⎽⎽⎽⎽ ⎜ ╱ 6 ⎟
╱ 1 ⎜ ╲╱ a ⎟ 3⋅a + 2⋅b⋅x ╱
1 ⎜ ╲╱ a ⎟
╱ ── ⋅log⎜x + ────────────────⎟ + ──────────────────────────── - ╱
── ⋅log⎜x + ────────────────⎟
╱ 6 ⎝ 2⋅b ⎠ 2 2 2 3 4 ╱
6 ⎝ 2⋅b ⎠
╲╱ a 2⋅a ⋅b ⋅x + 4⋅b⋅x⋅a + 2⋅a ╲╱ a
In [8]: factor(cancel(integrate(1/(x*(a+b*x)**3), x).diff(x)))
Out[8]:
1
────────────
3
x⋅(a + b⋅x)
I've also included a test. See https://github.com/sympy/sympy/pull/297.
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