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How can you use the tabular method to integrate xcos(x^2)

  1. Aug 2, 2017 #1
    1. The problem statement, all variables and given/known data
    This is not a homework but since asked me I'm posting it here. I know how to intergrate by parts and can do this using formula
    But I'd like to do this using the tabular method

    Question
    Integrate xcos(x^2) using tabular method


    2. Relevant equations
    The table with derivative on one volume and integral on the other column

    3. The attempt at a solution
    I know we can differentiate the one which is harder to intergrate so I integrated the x and differentiated cos(x^2)

    So I get -2sin(x^2) for the derivative column and (x^2)/2 on the intergral side
    When I multiply the results as said in tabular method and integrate the last portion, I get

    (X^2)/2 * cos(x^2) -2 integrated by sin(x^2) * (x^2)/2
     
    Last edited by a moderator: Aug 2, 2017
  2. jcsd
  3. Aug 2, 2017 #2
    The tabular method is integration by parts. It is just organizing the steps into a table. If you understand the formula than there is no need to make a table.
    The first derivative is ##-2x\text{sin}(x^{2})## not ##-2\text{sin}(x^{2})##. I don't think this is a good method to solve this problem though. This integral is relatively trivial using the u-substitution ##u=x^{2}##.
     
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