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Integral Help

  1. Feb 16, 2013 #1
    1. The problem statement, all variables and given/known data
    solve the integral.


    2. Relevant equations
    integral (sec(x)^2 / 4+tan(x)^2)


    3. The attempt at a solution
    i tried replacing the numerator with the trig identity: tan(x)^2 + 1 -- but not sure what else to try.
     
  2. jcsd
  3. Feb 16, 2013 #2
    There is a very obvious substitution you can do here.
     
  4. Feb 16, 2013 #3
    Consider the derivatives of trigonometric functions.
     
  5. Feb 16, 2013 #4
    was the step i performed correct?
     
  6. Feb 16, 2013 #5

    SammyS

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    No.

    What is the derivative of tan(x) ?
     
  7. Feb 16, 2013 #6
    What is d/dx (tanx)?
    Edit: or what sammy says :)
     
  8. Feb 16, 2013 #7
    Also, be careful that an integral is not the same thing as an antiderivative.
     
  9. Feb 16, 2013 #8

    HallsofIvy

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    The first thing I would do is replace sec2(x) with 1/cos2(x) and replace tan2(x) with sin2(x)/cos2(x).
     
  10. Feb 16, 2013 #9


    I wouldn't do this, but I would take a look at tanx and what the derivative is, it does become pretty hard though and you need a trig substitution afterwards, I think I did this exact problem before.
     
  11. Feb 17, 2013 #10
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