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Homework Help: Integration By Parts?

  1. Mar 21, 2010 #1
    Integration By Parts???

    1. The problem statement, all variables and given/known data
    int.arctan(2x)dx


    2. Relevant equations
    Integration By Parts


    3. The attempt at a solution

    In the attached image is the original problem with the ansewer I came up with using integration by parts and then a v=sub. later in the problem I did not want to post additional steps because it turned out to be a longer problem than I thought Just curious if someone could confirm my ansewer and if it is incorrect I will post the work to help see where I messed up. thanks a ton.
     

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  3. Mar 21, 2010 #2

    Dick

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    Science Advisor
    Homework Helper

    Re: Integration By Parts???

    I differentiated your antiderivative and I didn't get arctan(2x). If you want to check your work in the future, you could try that too. You can often get a clue where you messed up by looking at that as well.
     
  4. Mar 21, 2010 #3
    Re: Integration By Parts???

    thanks I will see if I can figure it out.
     
  5. Mar 21, 2010 #4
    Re: Integration By Parts???

    Yeah i almost got the same thing, except for the (1/4) looks like just a u-sub

    Integral of arctan(2x) dx..... u=2x du=2dx dx=(1/2)du

    so now we have (1/2) integ arctan(u) du

    leave the (1/2) out in front as a constant and I got u*arctan(u)-ln(sqrt(1+u^2))

    plug everything back in and i got x*arctan(2x)-(1/2)ln(sqrt(1+4x^2)) .... but I just used a table for arctan(u)
     
    Last edited: Mar 21, 2010
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