Alexey
Posts:
266
Registered:
6/14/08


Integrate bug in v 9.0.0
Posted:
Feb 2, 2013 1:15 AM


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

