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Re: Can somebody integrate this function ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112574] Re: Can somebody integrate this function ?
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Mon, 20 Sep 2010 05:44:41 -0400 (EDT)

Risch?? My Mathematica 7.0.1 does not recognize that as a built-in 
function name.

On 9/19/2010 5:37 AM, Emu wrote:
> On Sep 18, 9:24 pm, c r<riemannchristof... at gmail.com>  wrote:
>> Can somebody try this in your version of Mathematica ?
>>
>> Integrate[(5/12) (-1 + z) (y^2 - 3 z^2) (27 y^4 - 12 Sqrt[3] y^5 +
>>      4 y^6 + 18 y^2 (3 - 2 z) z^2 + 3 (3 - 2 z)^2 z^4 +
>>      4 Sqrt[3] y^3 z^2 (-3 + 2 z)), z]
>>
>> Something is definitely wrong with my version of Mathematica (7).
>
> Here's an alternative answer
>
> In[10]:= integrand = (5/12)*(-1 + z)*(y^2 - 3*z^2)*(27*y^4 -
>       12*Sqrt[3]*y^5 + 4*y^6 + 18*y^2*(3 - 2*z)*z^2 +
>       3*(3 - 2*z)^2*z^4 + 4*Sqrt[3]*y^3*z^2*(-3 + 2*z));
>
> In[11]:= Risch[integrand, z]
>
> Out[11]= -((45 y^6 z)/4) + 5 Sqrt[3] y^7 z - (5 y^8 z)/3 + (
>   45 y^6 z^2)/8 - 5/2 Sqrt[3] y^7 z^2 + (5 y^8 z^2)/6 + (
>   15 y^4 z^3)/4 - (10 y^5 z^3)/Sqrt[3] + (5 y^6 z^3)/3 + (
>   15 y^4 z^4)/16 + (5 y^5 z^4)/Sqrt[3] - (5 y^6 z^4)/4 + (
>   45 y^2 z^5)/4 - 3 Sqrt[3] y^3 z^5 - 3 y^4 z^5 + (
>   2 y^5 z^5)/Sqrt[3] - (115 y^2 z^6)/8 + (25 y^3 z^6)/(2 Sqrt[3]) + (
>   135 z^7)/28 + (25 y^2 z^7)/7 - 10/7 Sqrt[3] y^3 z^7 - (
>   315 z^8)/32 + (5 y^2 z^8)/8 + (20 z^9)/3 - (3 z^10)/2
>
> In[12]:= D[%, z] -
>    5/12 (-1 + z) (y^2 - 3 z^2) (27 y^4 - 12 Sqrt[3] y^5 + 4 y^6 +
>       18 y^2 (3 - 2 z) z^2 + 3 (3 - 2 z)^2 z^4 +
>       4 Sqrt[3] y^3 z^2 (-3 + 2 z)) // Together
>
> Out[12]= 0
>
> In[13]:= PolynomialQ[%%, z]
>
> Out[13]= True
>
> Note that the answer from Integrate is correct.
>
> In[17]:= Integrate[integrand, z];
>
> In[18]:= D[%, z] - integrand // Simplify
>
> Out[18]= 0
>

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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