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Re: Please explain this weird Integrate result


"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 



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