Comment #12 on issue 1280 by [email protected]: integrate(1/((a-x)*(b-x)),
x) is giving too complex results (probably correct)
http://code.google.com/p/sympy/issues/detail?id=1280
Now I'm not so sure that unequivocally calling apart() before integrating
rational functions is such a good idea. The reason is that it can result
in more logarithms than before. For example (the integral of tan(x)
recursively integrates a rational function u/(-u**2 + 1)
Before:
In [1]: integrate(tan(x), x)
Out[1]:
⎛ 2 ⎞
-log⎝sin (x) - 1⎠
─────────────────
2
After:
In [3]: integrate(tan(x), x)
Out[3]:
log(2⋅sin(x) - 2) log(2⋅sin(x) + 2)
- ───────────────── - ─────────────────
2 2
This leads to less nice results from dsolve():
Before:
In [2]: dsolve(f(x).diff(x)/tan(x) - f(x) - 2)
Out[2]:
C₁
f(x) = ──────────────── - 2
_____________
╱ 2
╲╱ sin (x) - 1
After:
In [1]: dsolve(f(x).diff(x)/tan(x) - f(x) - 2)
Out[1]:
C₁
f(x) = ───────────────────────────── - 2
____________ ____________
╲╱ sin(x) - 1 ⋅╲╱ sin(x) + 1
On the other hand, there is no question that this is preferable for
1/((x-a)*(x-b)*(x-c)), because it takes forever without it and returns
instantly with it.
Perhaps a better solution would be to investigate why 1/((x-a)*(x-b)*(x-c))
is so slow, and see if it can't be fixed directly.
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