Results 1 to 2 of 2

Math Help - integration by parts

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    65

    integration by parts

    Use integration by parts to find the integral.

    \int t^2*\exp{3t} dt
    u=t^2 v'=\exp{3t}
    u'=2t v=\frac{\exp{3t}}{3}
    \frac{1}{3}t^2\exp{3t}-\int\frac{2t\exp{3t}}{3}dt =\frac{1}{3}t^2\exp{3t}-\frac{2}{3}\int t\exp{3t} dt

    u=t v'=\exp{3t}
    u'=1 v=\frac{\exp{3t}}{3}


    \frac{1}{3}t^2\exp{3t}-\frac{2}{3}(\frac{1}{3}t\exp{3t}-\int\frac{1}{3}\exp{3t} dt)
    \frac{1}{3}t^2\exp{3t}-\frac{2}{3}(\frac{1}{3}t\exp{3t}-\frac{1}{3}*\frac{1}{3}\exp{3t})+C

    To clean this up a bit...
    \frac{1}{3}t^2\exp{3t}-\frac{2}{3}(\frac{1}{3}t\exp{3t}-\frac{1}{3}*\frac{1}{3}\exp{3t})+C

    \frac{1}{3}t^2\exp{3t}-\frac{2}{9}t\exp{3t}-\frac{1}{3}\exp{3t}+C=

    \frac{\exp{3t}}{3}(t^2-\frac{2}{9}t-1)

    Did I do all of that alright? It was not very easy to check with differentiation.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    The last term should be 2/29 e^(3t)

    not that hard to differentiate
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: January 11th 2012, 03:30 PM
  2. Replies: 8
    Last Post: September 2nd 2010, 01:27 PM
  3. Replies: 0
    Last Post: April 23rd 2010, 04:01 PM
  4. Integration by Parts!
    Posted in the Calculus Forum
    Replies: 7
    Last Post: January 22nd 2010, 04:19 AM
  5. Replies: 1
    Last Post: February 17th 2009, 07:55 AM

Search Tags


/mathhelpforum @mathhelpforum