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Homework Help: Integral rational function

  1. Mar 15, 2013 #1
    1. The problem statement, all variables and given/known data
    evaluate the integral.

    2. Relevant equations

    [itex]\displaystyle\int {\frac{1}{secx+tanx} dx}[/itex]

    3. The attempt at a solution
    can i just do ln|secx + tanx| ??
  2. jcsd
  3. Mar 15, 2013 #2


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    Staff Emeritus
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    Probably not.

    What's the derivative of ln|secx + tanx| ?

    Added in Edit:

    Write the tangent in terms of sine & cosine and the secant as the reciprocal of the cosine.
    Last edited: Mar 15, 2013
  4. Mar 15, 2013 #3


    Staff: Mentor

    No. You're making the same mistake you made in this thread: https://www.physicsforums.com/showthread.php?t=678488.

    It is NOT TRUE that
    $$ \int \frac{dx}{f(x)} = ln|f(x)| + C$$

    The above is true only if f(x) = x, which is certainly not the case here.
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