Results 1 to 2 of 2

Math Help - Integration by Parts

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    13

    Integration by Parts

    I have to integrate x times the square root of (x+3) and tried it using integration by parts. If u=x, du=dx, and v=the integration of the square root of (x+3), which is 2/3 times (x+3) raised to the 3/2 power, right?

    So, the answer works out to 2/3x times (x+3)^3/2 minus 2/3 times (x+3)^3/2, right?

    Also, is the conventional way to solve this integration by parts, or by substitution? I want to know because the answer that you get by u-sub looks a lot different from my answer, and I need to know in case on a multiple choice exam, the test-maker has decided to solve it using u-sub. I thought that you generally don't use u-sub unless you have the derivative of the function (in this case, we have an extra x, which seems to me a cue to not use u-sub).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,623
    Thanks
    428
    Quote Originally Posted by jaijay32 View Post
    I have to integrate x times the square root of (x+3) and tried it using integration by parts. If u=x, du=dx, and v=the integration of the square root of (x+3), which is 2/3 times (x+3) raised to the 3/2 power, right?

    So, the answer works out to 2/3x times (x+3)^3/2 minus 2/3 times (x+3)^3/2, right?

    Also, is the conventional way to solve this integration by parts, or by substitution? I want to know because the answer that you get by u-sub looks a lot different from my answer, and I need to know in case on a multiple choice exam, the test-maker has decided to solve it using u-sub. I thought that you generally don't use u-sub unless you have the derivative of the function (in this case, we have an extra x, which seems to me a cue to not use u-sub).
    parts is not necessary ...

    \int x\sqrt{x+3} \, dx

    u = x+3

    x = u-3

    du = dx

    \int (u-3)\sqrt{u} \, du

    \int u^{\frac{3}{2}} - 3u^{\frac{1}{2}} \, du

    finish
    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: 7
    Last Post: January 22nd 2010, 03:19 AM
  5. Replies: 1
    Last Post: February 17th 2009, 06:55 AM

Search Tags


/mathhelpforum @mathhelpforum