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MathGroup Archive 2007

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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


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