e^x / (1-2e^x)^3 dx

i replaced (1-2e^x) with a random letter in my case i used "p"

i ended up with the answer: 1 / 4(1-2e^x)² + C

however it doesnt look right to me, can anyone confirm if i am right or wrong?

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- Apr 5th 2012, 08:23 AMbobmarly12345intergral of e^x / (1-2e^x)^3 dx help
e^x / (1-2e^x)^3 dx

i replaced (1-2e^x) with a random letter in my case i used "p"

i ended up with the answer: 1 / 4(1-2e^x)² + C

however it doesnt look right to me, can anyone confirm if i am right or wrong? - Apr 5th 2012, 08:30 AMProve ItRe: intergral of e^x / (1-2e^x)^3 dx help
First note that $\displaystyle \displaystyle \begin{align*} \int{\frac{e^x}{\left(1 - 2e^x\right)^3}\,dx} = -\frac{1}{2}\int{\frac{-2e^x}{\left(1 - 2e^x\right)^3}\,dx} \end{align*}$.

Now make the substitution $\displaystyle \displaystyle \begin{align*} u = 1 - 2e^x \implies du = -2e^x\,dx \end{align*}$ and the integral becomes

$\displaystyle \displaystyle \begin{align*} -\frac{1}{2}\int{\frac{1}{u^3}\,du} = -\frac{1}{2}\int{u^{-3}\,du} \end{align*}$.

I'm sure you can go from here :)

Edit: On closer inspection of your original post, you got the answer right :) - Apr 5th 2012, 08:36 AMbiffboyRe: intergral of e^x / (1-2e^x)^3 dx help
It is correct. You can check by seeing whether you get back to the question when you differentiate your answer.