Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Not Clear on the Concept
Replies: 3   Last Post: Apr 10, 2013 5:27 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
magidin@math.berkeley.edu

Posts: 11,117
Registered: 12/4/04
Re: Not Clear on the Concept
Posted: Apr 9, 2013 1:25 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Monday, April 8, 2013 11:27:54 PM UTC-5, MNM wrote:
> Greetings,
>
> I know this may be a realatively stupid question, but it's unclear as to why for me.
>
> According to the full solution from Wolfram Alpha, when integrating (e^2x)/(1+e^x) and (e^3x)/(1+e^x), the substitution u=e^x is made. However, the numerators are u and u^2 respectively.



> Why is the power reduced by one upon substitution?

Because e^{2x} = (e^x)(e^x), and e^{3x} = (e^x)^2(e^x). If you set u=e^x, then du = e^xdx. So:

e^{2x}dx/(1+e^x) = (e^x)(e^x dx)/(1+e^x) = (u du)/(1+u)

and

e^{3x}dx/(1+e^x) = (e^x)^2(e^x dx)/(1+e^x) = u^2 du/(1+u)

--
Arturo Magidin




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.