Results 1 to 8 of 8

Math Help - Hard Integral

  1. #1
    Member
    Joined
    Sep 2006
    Posts
    221

    Hard Integral

    Find the following integral:

    \int{\frac{e^{-x}}{\sqrt{x}}~dx}

    Unable to use integration by parts I believe for this problem..
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Ideasman View Post
    Find the following integral:

    \int{\frac{e^{-x}}{\sqrt{x}}~dx}

    Unable to use integration by parts I believe for this problem..
    is the integral indefinite? if so, there is no solution in elementary functions, you would need the erf function
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Jan 2008
    From
    Montreal
    Posts
    311
    Awards
    1
    not sure if this will be of any help, but you could also express [tex] e^{-x} as an infinite series then integrate it out.

    so you would have:

    \int \frac{\sum^{\infty}_{n=0} \frac{-x^n}{n!}}{\sqrt{x}} dx

    = \int \sum^{\infty}_{n=0} \frac{-x^{n-0.5}}{n!} dx

    = \sum^{\infty}_{n=0} \frac{-x^{n+0.5}}{(n+0.5)n!} +C
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,212
    Thanks
    419
    Awards
    1
    Quote Originally Posted by Ideasman View Post
    Find the following integral:

    \int{\frac{e^{-x}}{\sqrt{x}}~dx}

    Unable to use integration by parts I believe for this problem..
    If this is supposed to be
    \int_0^{\infty} {\frac{e^{-x}}{\sqrt{x}}~dx}
    then this is a gamma function.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Jhevon View Post
    is the integral indefinite? if so, there is no solution in elementary functions, you would need the erf function
    ..
    Attached Thumbnails Attached Thumbnails Hard Integral-msp12.gif  
    Follow Math Help Forum on Facebook and Google+

  6. #6
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by topsquark View Post
    If this is supposed to be
    \int_0^{\infty} {\frac{e^{-x}}{\sqrt{x}}~dx}
    then this is a gamma function.

    -Dan
    yes, if we had limits like that, then a substitution would turn the integrand into  2e^{-u^2} which is fun to do...
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member PaulRS's Avatar
    Joined
    Oct 2007
    Posts
    571
    Quote Originally Posted by topsquark View Post
    If this is supposed to be
    \int_0^{\infty} {\frac{e^{-x}}{\sqrt{x}}~dx}
    then this is a gamma function.

    -Dan
    Yes

    Let u=\sqrt[]{x} then \int_0^{\infty} {\frac{e^{-x}}{\sqrt{x}}dx}=2\int_0^{\infty} {e^{-u^2}du} =\int_{-\infty}^{\infty} {e^{-u^2}du}=\sqrt[]{\pi}

    Gaussian integral - Wikipedia, the free encyclopedia
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    14
    The well known gaussian integral. There're lots of proofs of its result.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. hard integral
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 20th 2010, 02:46 PM
  2. Hard Integral
    Posted in the Calculus Forum
    Replies: 8
    Last Post: July 4th 2009, 06:03 AM
  3. hard integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 27th 2009, 05:44 AM
  4. Hard integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 24th 2009, 11:36 AM
  5. integral ... hard?
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 4th 2008, 07:07 PM

Search Tags


/mathhelpforum @mathhelpforum