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Integral evaluation problem

  1. Apr 25, 2010 #1
    Evaluate
    [tex]\int\frac{arctan(x)dx}{(1+x^2)^\frac{3}{2}}[/tex]
     
  2. jcsd
  3. Apr 25, 2010 #2

    arildno

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    Re: integral

    Make the substitution:
    [tex]x=\tan(u),\to\frac{dx}{du}=\frac{1}{\cos^{2}u}[/tex]
    Thus, we get:
    [tex]dx=\frac{du}{\cos^{2}(u)}[/tex]
    and insertion in your integral yields:
    [tex]\int\frac{arctan(x)}{(1+x^{2})^{\frac{3}{2}}}=\int{u}\cos(u)du[/tex]
     
  4. Apr 25, 2010 #3
    Re: integral

    your solution seems nice
    honestly i thought it is a hard one,becouse i picked it form "A coures of pure mathematics"
     
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