Re: Please explain this weird Integrate result

*To*: mathgroup at smc.vnet.net*Subject*: [mg60149] Re: Please explain this weird Integrate result*From*: "Carl K. Woll" <carlw at u.washington.edu>*Date*: Sun, 4 Sep 2005 03:02:16 -0400 (EDT)*Organization*: University of Washington*References*: <dfbevv$inu$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

"Jose Reckoner" wrote: > > Expand[Integrate[(2*x)/(2*x - 1), x]] > > gives > > -1/2 + x + Log[-1 + 2*x]/2 > > But, > > Expand[Integrate[1 + 1/(-1 + 2*x), x]] > > gives > > x + Log[-1 + 2*x]/2 > > even though > > (2*x)/(2*x - 1) == 1 + 1/(-1 + 2*x) > > Where did the extra -1/2 in the first result come from? > Indefinite integrals are only defined up to a constant, hence there is nothing wrong mathematically going on here. Check that the integrals are correct by taking derivatives: In[11]:= D[-1/2 + x + Log[-1 + 2*x]/2,x]//Together Out[11]= (2 x)/(-1+2 x) In[12]:= D[x + Log[-1 + 2*x]/2,x]//Together Out[12]= (2 x)/(-1+2 x) Carl Woll Wolfram Research