       Re: Indefinate integrals, erroneus Natural log?

• To: mathgroup at smc.vnet.net
• Subject: [mg77921] Re: Indefinate integrals, erroneus Natural log?
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Tue, 19 Jun 2007 07:01:47 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <f55oor\$j6f\$1@smc.vnet.net>

```David Rees 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:=
> \!\(\[Integral]\((xE\^\(2 x\))\) \[DifferentialD]x\)
> Out=
> \!\(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
>
> ((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

They are not. However, I strongly suspect that you made some typos while
entering the expressions. I am almost certain that, for the integrand,
what you wanted was "x times the base of the natural logarithm raised to
the power of 2 times x, that is "x*E^(2*x)" and not "the variable called
xE raised to the power of 2 times x," that is what you wrote.

Moreover, the regular lowercase letter "e" denotes nothing in
Mathematica: the base of the natural logarithm is written E (capital e).
(Note that you can also use some special character to enter or display
it. See the Basic Input palette.)

Also, multiplication is denoted by a space between the variable names or
by a star.

Having said that,

In:=
expr1 = Integrate[x*E^(2*x), x]
expr2 = (1/2)*x*E^(2*x) - (1/4)*E^(2*x)
Simplify[expr1 == expr2]

Out=
2 x    1    x
E    (-(-) + -)
4    2

Out=
2 x
E       1  2 x
-(----) + - E    x
4      2

Out=
True

Regards,
Jean-Marc

```

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