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Math Help - intergral of e^x / (1-2e^x)^3 dx help

  1. #1
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    intergral 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) + C
    however it doesnt look right to me, can anyone confirm if i am right or wrong?
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  2. #2
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    Re: intergral of e^x / (1-2e^x)^3 dx help

    Quote Originally Posted by bobmarly12345 View Post
    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) + C
    however it doesnt look right to me, can anyone confirm if i am right or wrong?
    First note that \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 \begin{align*} u = 1 - 2e^x \implies du = -2e^x\,dx \end{align*} and the integral becomes

    \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
    Last edited by Prove It; April 5th 2012 at 09:33 AM.
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  3. #3
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    Re: 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.
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