• To: mathgroup at smc.vnet.net
• Subject: [mg71465] Re: Why does this lead to an answer with complex numbers?
• From: "David W. Cantrell" <DWCantrell at sigmaxi.net>
• Date: Mon, 20 Nov 2006 02:43:46 -0500 (EST)
• References: <ejosmm\$n3k\$1@smc.vnet.net>

```aaronfude at gmail.com wrote:
> The expression is
>
> \!\(FullSimplify[
>     Assuming[\[Beta] > 0 && \[Beta] < Pi/2,
>       Integrate[\(-Log[\@\(1 + x\^2\) - 1/11*x\ ]\), \ x]]]\)

Maybe you intended to use x rather than Beta in your assumption. In any

Mathematica will sometimes gives complex answers, even when you wish they
were real, and using assumptions may not help. Consider the simple example

In[90]:= Assuming[x < 0, Integrate[1/x, x]]

Out[90]= Log[x]

Since x < 0, Log[x] will be complex. Students in beginning calculus would
likely have given the antiderivative as Log[Abs[x]].

Back to your example, the antiderivative given by Mathematica is complex,
as you noted, but the imaginary part is merely _constant_, namely

- 11 Log[30]/(2 Sqrt[30]) I.

Thus, if you just add 11 Log[30]/(2 Sqrt[30]) I to Mathematica's result,
you have an antiderivative which is real for all real x.

David

```

• Prev by Date: Re: Coercion into series
• Next by Date: Summations in a Text Cell