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Integrating by parts

  1. Mar 19, 2013 #1
    1. The problem statement, all variables and given/known data
    ∫arctan(√x)dx.

    Using the substitution √x=t:
    ∫arctan(√x)dx = ∫arctan(t)dt2

    This is what ive got written in a solution manual. I dont see why the dt would be squared. Could anyone care explaining me? thanks
     
  2. jcsd
  3. Mar 19, 2013 #2

    HallsofIvy

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    The substitution [itex]t= \sqrt{x}[/itex] is the same (for positive x and t) as [itex]t^2= x[/itex] so that [itex]dx= d(t^2)= 2tdt[/itex].

    What is done here is "integration by substitution". The result is [itex]2\int arctan(t) tdt[/itex] which can now be done by "integration by parts".
     
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