Results 1 to 2 of 2

Math Help - Integration By Parts?

  1. #1
    Super Member
    Joined
    Sep 2007
    Posts
    528
    Awards
    1

    Integration By Parts?

    \int 3xe^{2x^2} \ \mathrm{d}x

    How do you integrate this? Thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,

    Quote Originally Posted by Air View Post
    \int 3xe^{2x^2} \ \mathrm{d}x

    How do you integrate this? Thanks in advance.
    By the substitution : t=2x^2


    How can you know it's this way ? Because you can notice that the derivative of 2x^2 is 4x.

    In front of the exponential, we have 3x=\frac 34 (4x)

    So you have something like k \int u'(x)e^{u(x)} dx, k is a constant (here \frac 34)
    Here, two methods :
    - you substitute v=u(x)
    - you recognize the derivative of e^{u(x)}

    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