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Integral of tan^3(x)

  1. Feb 29, 2012 #1
    1. The problem statement, all variables and given/known data

    ∫[itex]tan^{3}[/itex]x dx

    2. Relevant equations

    [itex]tan^{2}x[/itex]+1 = [itex]sec^{2}[/itex]x

    [itex]tan^{3}[/itex]x = [itex]tan^{2}[/itex]x * tan(x)

    3. The attempt at a solution

    ∫[itex]tan^{2}[/itex]x * tan(x) dx

    ∫([itex]sec^{2}[/itex]x -1 ) tan(x) dx

    ∫([itex]sec^{2}[/itex]xtan(x) -∫tan(x)

    ∫u du - [itex]sec^{2}[/itex]x

    [itex]u^{2}[/itex]/2 - [itex]sec^{2}[/itex]x

    [itex]tan^{2}[/itex]x/2 - [itex]sec^{2}[/itex]x
  2. jcsd
  3. Feb 29, 2012 #2
    Oh damn. I just realized integral of tanx is ln|secx|.

    I got it wrong on my test :(
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