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Math Help - Not sure how to do this integral.

  1. #1
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    Not sure how to do this integral.

    Here she is.

    <br />
\int \frac {1}{x^3}e^\frac{1}{x}<br />

    Thanks.
    Last edited by Gotovina7; April 16th 2008 at 06:15 PM.
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Gotovina7 View Post
    Here it is.

     \int \frac {1}{x^3}e^\frac{1}{x}

    Thanks.
    Using power series rewrite it as \int\frac{\sum_{n=0}^{\infty}\frac{\bigg(\frac{1}{  x}\bigg)^n}{n!}}{x^3}dx\Rightarrow\int\frac{\sum_{  n=0}^{\infty}\frac{x^{-n}}{n!}}{x^3}dx

    then rewrite it as \int\sum_{n=0}^{\infty}\frac{x^{-n-3}}{n!}dx

    integrating we get \int{\frac{e^{\frac{1}{x}}}{x^3}}dx=\sum_{n=0}^{\i  nfty}\frac{x^{-n-2}}{(-n-2)n!}
    or you could just use parts whichever way your teacher wants
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  3. #3
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    Quote Originally Posted by Gotovina7 View Post
    Here it is.

     \int \frac {1}{x^3}e^\frac{1}{x}

    Thanks.
    Make the obvious substitution u = \frac{1}{x} \Rightarrow dx = -x^2 \, du.

    Then the integral becomes \int u e^u \, du.

    Now use integration by parts.
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  4. #4
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    Ooh, I got it now! Thanks guys!
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  5. #5
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    How would I do this one?

     \int \frac{1}{e^x+2 \sqrt{e^x}+1}dx

    Thanks
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  6. #6
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Gotovina7 View Post
    How would I do this one?

     \int \frac{1}{e^x+2 \sqrt{e^x}+1}dx

    Thanks
    Next time start a new post but does this help \int\frac{1}{e^{x}+2e^{\frac{x}{2}}+1}dx=\int\frac  {1}{(e^{\frac{x}{2}}+1)^2}dx?
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  7. #7
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    Quote Originally Posted by Gotovina7 View Post
    How would I do this one?

     \int \frac{1}{e^x+2 \sqrt{e^x}+1}dx

    Thanks
    Note: New question => New thread.

    Make the obvious substitution u^2 = e^x \Rightarrow 2u \frac{du}{dx} = e^x = u^2 \Rightarrow dx = \frac{2 \, du}{u}.

    Then the integral becomes (after a little bit of algebra): 2 \int \frac{du}{(u+1)^2 u}.

    Now use partial fractions etc.
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  8. #8
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    Ooh, I see it now. Thanks guys. Sorry about the post.
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  9. #9
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Gotovina7 View Post
    Need help with another one, scroll down
    please do not delete your question
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  10. #10
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    Quote Originally Posted by Jhevon View Post
    please do not delete your question
    Yeah sorry, its back up.
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