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Homework Help: Integration problem

  1. Oct 10, 2004 #1
    How does one integrate
    [tex]\int\arctan 4t\,dt[/tex]
    ?

    This is out of a section on integration by parts. Maybe that would help but I don't see any "parts." I only see one, the arctan.
     
  2. jcsd
  3. Oct 10, 2004 #2

    Math Is Hard

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    Let u = arctan4t
    dv = dt
     
  4. Oct 10, 2004 #3
    Thank you so much. Please tell me if I did this correctly.
    Integration by Parts:
    [tex]\int u\,dv = uv - \int v\,du [/tex]

    [itex]u = \arctan 4t , \,dv = dt , v = t\,dt , \,du = \frac{4}{16t^2 + 1}[/itex]
    [tex]\int\arctan 4t\,dt = t\arctan 4t - \int\frac{4t}{16t^2 + 1}\,dt = t\arctan 4t - \frac{1}{8}\ln(16t^2 + 1) + C [/tex]
     
  5. Oct 10, 2004 #4

    Math Is Hard

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    yup! looks good to me!
     
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