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Re: Integrate bug in v 9.0.0
Posted:
Feb 4, 2013 10:23 PM


On Saturday, February 2, 2013 12:15:44 AM UTC6, Alexey Popkov wrote: > In version 9.0.0 the following integral is reported as divergent: > > > > In[71]:= Integrate[x^2/(x^2  x0^2), {x, x1, x2}, > > Assumptions > x0 > x2 > x1 >= 0] > > > > During evaluation of In[71]:= Integrate::idiv: Integral of x^2/(x^2x0^2) > > does not converge on {x1,x2}. >> > > > > Out[71]= Integrate[x^2/(x^2  x0^2), {x, x1, x2}, > > Assumptions > x0 > x2 > x1 >= 0] > > > > Versions 8.0.4 and 5.2 give equivalent expressions: > > > > In[2]:= Integrate[x^2/(x^2  x0^2), {x, x1, x2}, > > Assumptions > x0 > x2 > x1 >= 0] > > > > Out[2]= x1 + x2 + x0 ArcTanh[(x0 (x1  x2))/(x0^2  x1 x2)] > > > > In[9]:= > > Integrate[x^2/(x^2x0^2),{x,x1,x2},Assumptions>x0>x2>x1>=0] > > Out[9]= > > x1+x2+1/2 x0 (Log[x0+x1]+Log[x0x2]Log[(x0x1) (x0+x2)]) > > > > In[8]:= FullSimplify[x1 + x2 + > > 1/2 x0 (Log[x0 + x1] + Log[x0  x2]  > > Log[(x0  x1) (x0 + x2)]) == x1 + x2 + > > x0 ArcTanh[(x0 (x1  x2))/(x0^2  x1 x2)], > > Assumptions > x0 > x2 > x1 >= 0] > > > > Out[8]= True > > > > Alexey
Appears to be substantially the same underlying issue as was reported here.
http://mathematica.stackexchange.com/questions/18348/mathematica9cannotsolvethisintegralmathematica8couldisthisabug
It is provisionally fixed in the version currently under development.
Daniel Lichtblau Wolfram Research



