Updates:
Labels: Integration
Comment #3 on issue 2066 by asmeurer: integration of
c**2*exp(c/x)/(x**3*(1+exp(c/x)**2)) fails
http://code.google.com/p/sympy/issues/detail?id=2066
Because I can't resist showing off my work, I can't help but mention that
this is going to be much more awesome with the new Risch Algorithm
integrator (issue 2010):
In [1]: var('c')
Out[1]: c
In [2]: f = c**2*exp(c/x)/(x**3*(1+exp(c/x))**2)
In [3]: f
Out[3]:
c
─
2 x
c ⋅ℯ
────────────
2
⎛ c⎞
⎜ ─⎟
3 ⎜ x⎟
x ⋅⎝1 + ℯ ⎠
In [4]: integrate(f, x)
Out[4]:
⎛ ⎛ c⎞ c ⎛ c⎞ c ⎞
⎜ ⎜ ─⎟ ─ ⎜ ─⎟ ─ ⎟
⎜ ⎜ x⎟ x ⎜ x⎟ x ⎟
2 ⎜x⋅log⎝1 + ℯ ⎠ x⋅ℯ ⋅log⎝1 + ℯ ⎠ c⋅ℯ ⎟
c ⋅⎜────────────── + ──────────────── - ──────────────⎟
⎜ c c c⎟
⎜ ─ ─ ─⎟
⎜ 2 2 x 2 2 x 2 2 x⎟
⎝x⋅c + x⋅c ⋅ℯ x⋅c + x⋅c ⋅ℯ x⋅c + x⋅c ⋅ℯ ⎠
In [5]: risch_integrate(f, x)
Out[5]:
⎛ c⎞
⎜ ─⎟
⎜ 2 2 x⎟ c c
-2⋅log(x) + log⎝x + x ⋅ℯ ⎠ + ──────── - ─
c x
─
x
x + x⋅ℯ
In [6]: %timeit integrate(f, x)
1 loops, best of 3: 36.4 s per loop
In [7]: %timeit risch_integrate(f, x)
1 loops, best of 3: 313 ms per loop
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