Author Topic: Anti Dif Help (Read 851 times) Tweet Share

patricktsmith · « **on:** August 28, 2011, 05:52:54 pm »

Anti Dif of

e^3x/(e^x)-1 by letting u = (e^x)-1

b^3 · « **Reply #1 on:** August 28, 2011, 06:00:13 pm »

$\int \frac{e^{3x}}{e^{x}-1}dx$
let $u=e^{x}-1$
then $e^{x}=u+1$ and $\frac{du}{dx}=e^{x}$
so $dx=\frac{du}{e^{x}}$
$\int \frac{e^{3x}}{e^{x}-1}dx=\int \frac{e^{3x}}{u}\frac{du}{e^{x}}$
$=\int \frac{e^{2x}}{u}du$
$=\frac{(u+1)^{2}}{u}du$
$=\int \frac{u^{2}+2u+1}{u}du$
$=\int u+2+\frac{1}{u}du$
$=\frac{u^{2}}{2}+2u+ln(|u|)+c$
$=\frac{(e^{x}-1)^{2}}{2}+2(e^{x}-1)+ln(|e^{x}-1|)+c$
expand it $ln(|e^{x}-1|)+\frac{e^{2x}}{2}+e^{x}-\frac{3}{2}+c$

EDIT: Expanded

paulsterio · « **Reply #2 on:** August 29, 2011, 12:47:43 pm »

good work b^3

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Author Topic: Anti Dif Help (Read 851 times) Tweet Share

patricktsmith

Anti Dif Help

b^3

Re: Anti Dif Help

paulsterio

Re: Anti Dif Help

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