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Homework Help: More integration by subsitution

  1. Oct 10, 2006 #1
    I (now) know that I can check the following by differentiating my answer, but I don't trust my differentiation.

    Problem is as follows:

    [tex]\int\tan^4{3x}\sec^2{3x}dx[/tex]
    I assigned u=tan(3x), du=3sec^2(3x) and got that integral in terms of u:
    [tex]\frac{1}{3}\int u^4du[/tex]
    [tex] =\frac{1}{3}\times\frac{u^5}{5}+C[/tex]
    [tex] =\frac{\tan^5(3x)}{15}+C[/tex]

    I think that differentiates into what's in the original integral, but as I haven't differentiated anything that looks like that for a while now, I'd appreciate some feedback.

    Thanks!
     
  2. jcsd
  3. Oct 10, 2006 #2
    thats correct
     
  4. Oct 10, 2006 #3
    Thank you very much.
     
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