Results 1 to 10 of 10

Math Help - integration by parts

  1. #1
    Junior Member
    Joined
    May 2010
    Posts
    39

    integration by parts

    Am i doing something wrong? I cant seem to spot my mistake, the answer is in red (given by my teacher).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    \int x^3 \cdot e^{\frac{x^2}{2}} \, dx

    t = \frac{x^2}{2}

    dt = x \, dx

    2 \int x \cdot \frac{x^2}{2} \cdot e^{\frac{x^2}{2}} \, dx

    substitute ...

    2 \int t \cdot e^{t} \, dt

    now do parts
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    May 2010
    Posts
    39
    Quote Originally Posted by skeeter View Post
    \int x^3 \cdot e^{\frac{x^2}{2}} \, dx

    t = \frac{x^2}{2}

    dt = x \, dx

    2 \int x \cdot \frac{x^2}{2} \cdot e^{\frac{x^2}{2}} \, dx

    substitute ...

    2 \int t \cdot e^{t} \, dt

    now do parts
    thanks! just wondering, where did i go wrong in my first answer?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by gomes View Post
    thanks! just wondering, where did i go wrong in my first answer?
    e^{\frac{x^2}{2}} does not have an elementary antiderivative ... so, it cannot be chosen as "dv"
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3
    let  u = x^{2}

    and  dv = x e^{x^{2}/2}
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,313
    Thanks
    1291
    While, in differentiating something like e^{x^2} you can just multiply by the derivative of x^2, to get 2xe^{x^2}, when integrating you cannot just divide by the derivative- it must already be in the integral.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    May 2010
    Posts
    39
    thanks everyone, very helpful! erm, could someone clarify for me: how do i know if something has an elementary antiderivative or not?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by gomes View Post
    thanks everyone, very helpful! erm, could someone clarify for me: how do i know if something has an elementary antiderivative or not?
    experience

    http://www.math.unt.edu/integration_bee/AwfulTruth.html
    Last edited by skeeter; May 30th 2010 at 01:50 PM. Reason: add link
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Super Member
    Joined
    Mar 2010
    Posts
    715
    Thanks
    2
    Quote Originally Posted by gomes View Post
    How do i know if something has an elementary antiderivative or not?
    Differential Galois theory.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Junior Member
    Joined
    May 2010
    Posts
    39
    Thanks everyone!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: January 11th 2012, 02:30 PM
  2. Replies: 8
    Last Post: September 2nd 2010, 12:27 PM
  3. Replies: 0
    Last Post: April 23rd 2010, 03:01 PM
  4. integration by parts
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 18th 2009, 06:21 AM
  5. Replies: 1
    Last Post: February 17th 2009, 06:55 AM

Search Tags


/mathhelpforum @mathhelpforum