Comment #6 on issue 1892 by mattpap: integrate(1/(x*(a+b*x)**3), x) fails
http://code.google.com/p/sympy/issues/detail?id=1892
btw. These are current results from polys11 branch:
In [1]: var('a,b')
Out[1]: (a, b)
In [2]: f = 1/(x*(a+b*x)**3)
In [3]: f
Out[3]:
1
────────────
3
x⋅(a + b⋅x)
In [4]: %time integrate(_, x)
CPU times: user 0.48 s, sys: 0.00 s, total: 0.48 s
Wall time: 0.51 s
Out[5]:
⎛ a⎞
log⎜x + ─⎟
log(x) 3⋅a + 2⋅b⋅x ⎝ b⎠
────── + ──────────────────────────── - ──────────
3 2 2 2 3 4 3
a 2⋅a ⋅b ⋅x + 4⋅b⋅x⋅a + 2⋅a a
In [6]: %time Add(*[ integrate(g, x) for g in apart(f, x).args ])
CPU times: user 0.34 s, sys: 0.00 s, total: 0.34 s
Wall time: 0.35 s
Out[7]:
log(x) log(a + b⋅x) 1 1
────── - ──────────── + ──────────── + ──────────────
3 3 2 2
a a a ⋅(a + b⋅x) 2⋅a⋅(a + b⋅x)
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