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[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
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[1]:=
expr1 = Integrate[x*E^(2*x), x]
expr2 = (1/2)*x*E^(2*x) - (1/4)*E^(2*x)
Simplify[expr1 == expr2]
Out[1]=
2 x 1 x
E (-(-) + -)
4 2
Out[2]=
2 x
E 1 2 x
-(----) + - E x
4 2
Out[3]=
True
Regards,
Jean-Marc