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

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 magidin@math.berkeley.edu Posts: 11,749 Registered: 12/4/04
Re: Not Clear on the Concept
Posted: Apr 9, 2013 1:25 AM

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

Date Subject Author
4/9/13 mark.n.mcallister
4/9/13 Virgil
4/9/13 magidin@math.berkeley.edu
4/10/13 me 154934