
Re: Not Clear on the Concept
Posted:
Apr 9, 2013 1:25 AM


On Monday, April 8, 2013 11:27:54 PM UTC5, 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

