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Re: Indefinate integrals, erroneus Natural log?

• To: mathgroup at smc.vnet.net
• Subject: [mg77897] Re: Indefinate integrals, erroneus Natural log?
• From: Norbert Marxer <marxer at mec.li>
• Date: Tue, 19 Jun 2007 06:40:44 -0400 (EDT)
• References: <f55oor$j6f$1@smc.vnet.net>

On 18 Jun., 13:02, "David Rees" <w3bdevilREM... at THISw3bdevil.com>
wrote:
> Hi,
>
> In preparation for a major exam tomorrow, I was just checking some of my
> answers to past-papers with mathematica, I fed it this input:
>
> In[117]:=
> \!\(\[Integral]\((xE\^\(2 x\))\) \[DifferentialD]x\)
> Out[117]=
> \!\(xE\^\(2\ x\)\/\(2\ Log[xE]\)\)
>
> I marked myself wrong and moved on to the next question, but I happened
> accross the actual mark-scheme which said I was correct. It gave this
> answer:
>
> ((1/2)xE^(2x))-(1/4)e^(2x)
>
> My Integral calculus isn't so strong, so I don't know if the additional
> natural log should be there, or if the two expressions are identical.
>
> Thanks

Hello

Note that you should have a space (or a multiplication operator)
between your variable x and the constant E (the base of the natural
logarithm).

The following input gives your expected output:

In[1]:=
Integrate[x*E^(2*x), x]

Out[1]=
E^(2*x)*(-(1/4) + x/2)

Whereas using the variable xE gives your (not expected) output:

In[2]:=
Integrate[xE^(2*x), x]

Out[2]=
xE^(2*x)/(2*Log[xE])

I hope this helps.

Best Regards
Norbert Marxer