1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integration by parts

  1. Sep 18, 2010 #1
    1. The problem statement, all variables and given/known data
    [tex] \int arctan(4t) [/tex]


    2. Relevant equations
    I know what the answer is to the problem but when i look at the solution i have no idea how they get from one step to the next.


    3. The attempt at a solution

    once we integrate by parts we get
    [tex] 1/4 U arctan(U) - 1/4 \int U/1+U^2 [/tex] where U= 4t

    from this they go to..

    [tex] 1/4 U arctan(U) - 1/8 \int 2U/1+U^2 [/tex]

    clearly a 2 was multiplied inside and a 1/2 on the outside of the integral, but why? and how? because the next step shown is..

    [tex] 1/4 (4t arctan(4t) - 1/8 ln 16t^2 + c [/tex]

    which is the answer..i get that 4t was substituted back in for U, but i dont understand how and why the 2 was put in the integral and the 1/2 outside of it, and how in the last step the 2U somehow is gone?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 18, 2010 #2

    jgens

    User Avatar
    Gold Member

    You should use parantheses to make your work clearer. Anyway, note that (1+u2)' = 2u. The two is multiplied (and divided) so that you can apply the substitution rule for integration.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Integration by parts
  1. Integration by parts (Replies: 6)

  2. Integration by parts (Replies: 8)

  3. Integration by Parts (Replies: 8)

Loading...