Re: Integrate bug in v 9.0.0

*To*: mathgroup at smc.vnet.net*Subject*: [mg129697] Re: Integrate bug in v 9.0.0*From*: danl at wolfram.com*Date*: Mon, 4 Feb 2013 22:24:43 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <keiaug$qqn$1@smc.vnet.net>

On Saturday, February 2, 2013 12:15:44 AM UTC-6, 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^2-x0^2) > > 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^2-x0^2),{x,x1,x2},Assumptions->x0>x2>x1>=0] > > Out[9]= > > -x1+x2+1/2 x0 (Log[x0+x1]+Log[x0-x2]-Log[(x0-x1) (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/mathematica-9-cannot-solve-this-integral-mathematica-8-could-is-this-a-bug It is provisionally fixed in the version currently under development. Daniel Lichtblau Wolfram Research