Hi,
On 6 October 2011 12:04, Mateusz Paprocki <matt...@gmail.com> wrote:
> Hi,
>
> On 6 October 2011 11:57, Scott <scotta_2...@yahoo.com> wrote:
>
>> How do I coerce integrate(a/(a**2+b*a+b*c*x**2),x) to yield.
>> This may be a double post.
>>
>> Sqrt[b] Sqrt[c] x
>> Sqrt[a] ArcTan[-------------------]
>> Sqrt[a] Sqrt[a + b]
>> -----------------------------------
>> Sqrt[b] Sqrt[a + b] Sqrt[c]
>>
>>
>>
>> Rather than:
>> var('x,a,b,c')
>> integrate(a/(a**2+b*a+b*c*x**2),x)
>>
>> a*((-b*c/(4*a*b**3*c**2 + 4*a**2*b**2*c**2))**(1/2)*log(x + (-b*c/
>> (4*a*b**3*c**2 + 4*a**2*b**2*c**2))**(1/2)*(2*a*b + 2*a**2)) - (-b*c/
>> (4*a*b**3*c**2 + 4*a**2*b**2*c**2))**(1/2)*log(x - (-b*c/
>> (4*a*b**3*c**2 + 4*a**2*b**2*c**2))**(1/2)*(2*a*b + 2*a**2))
>>
>
> I would start from making x, a, b,c real, e.g.:
>
> In [4]: var('a:c,x', real=True)
> Out[4]: (a, b, c, x)
>
> In [5]: integrate(a/(a**2+b*a+b*c*x**2),x)
>
> but this fails, see http://code.google.com/p/sympy/issues/detail?id=2718.
>
I fixed this issue (for now locally). The problem was with symbolic root
counting algorithm.
By making a, b, c positive, I was able to get the requested form of the
integral:
In [1]: var('a:c', positive=True)
Out[1]: (a, b, c)
In [2]: integrate(a/(a**2+b*a+b*c*x**2),x)
Out[2]:
⎛ ⎛ ___ 3/2 ⎞ ⎞
___ ⎜ x⋅⎝a⋅╲╱ b ⋅c + b ⋅c⎠ ⎟
╲╱ a ⋅atan⎜──────────────────────────────────────────────⎟
⎜ 3/2 ___ _______ ___ ___ _______⎟
⎝a ⋅╲╱ c ⋅╲╱ a + b + ╲╱ a ⋅b⋅╲╱ c ⋅╲╱ a + b ⎠
──────────────────────────────────────────────────────────
___ ___ _______
╲╱ b ⋅╲╱ c ⋅╲╱ a + b
In [3]: simplify(_)
Out[3]:
⎛ ___ ___ ⎞
___ ⎜ ╲╱ b ⋅╲╱ c ⋅x ⎟
╲╱ a ⋅atan⎜───────────────⎟
⎜ ___ _______⎟
⎝╲╱ a ⋅╲╱ a + b ⎠
───────────────────────────
___ ___ _______
╲╱ b ⋅╲╱ c ⋅╲╱ a + b
>
>
>>
>> Thanks
>>
>> Scott
>>
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>>
> Mateusz
>
Mateusz
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