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Re: (Not trivial) Definite Integration of a rational function


Offhand I'm not sure why this failed in 5.2, but it works in the development version:

In[1]:= Integrate[(2*x)/((x + 1)*(x^3 + 3*x^2 + 2*x + 1)), {x, 0, Infinity}] //Timing //InputForm

Out[1]//InputForm=
{0.85, -2*RootSum[1 + 2*#1 + 3*#1^2 + #1^3 & ,
   (Log[-#1] + 2*Log[-#1]*#1 + Log[-#1]*#1^2)/(2 + 6*#1 + 3*#1^2) & ]}

In[2]:= N[Last[%], 20]

                                      -20
Out[2]= 0.37121697526024703447 + 0. 10    I

Bhuvanesh,
Wolfram Research.


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