Re: Integral confusion

• To: mathgroup at smc.vnet.net
• Subject: [mg107291] Re: Integral confusion
• From: Simon <simonjtyler at gmail.com>
• Date: Mon, 8 Feb 2010 03:35:11 -0500 (EST)
• References: <hkm7d8\$os0\$1@smc.vnet.net>

```On Feb 7, 7:15 pm, Jon Joseph <josco.... at gmail.com> wrote:
> All: Is this integral wrong? If not could someone explain the minus sign
> inside the log?
>
> Integrate[1/(x + 1) - 1/(x + 6), x] // Simplify
>
> log(-2 (x + 1)) - log(2 (x + 6))
>
> Thanks, Jon.=

The integral is correct (just take its derivative and see).
>From the look of the unsimplified output
In[1]:= Integrate[1/(x + 1) - 1/(x + 6), x]
Out[1]= 5 (1/5 Log[-2 (1 + x)] - 1/5 Log[2 (6 + x)])
I think that Mathematica is doing a Together before the integral.
If you integrate each term separately, you get what you'd expect
In[2]:= Integrate[{1/(x + 1), -1/(x + 6)}, x]
Out[2]= {Log[1 + x], -Log[6 + x]}
But of course, the different branches of Log only differ by a
constant
-- which is exactly what indefinite integrals don't care about.
If x > 1, then you can simply factor out the minus sign using
In[3]:= Log[-1]
Out[3]= I \[Pi]

```

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