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Math Help - Explain the integral of tan...

  1. #1
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    Explain the integral of tan...

    Hi

    my book says the integral of tan x = ln |sec x|

    When i do it:

    tan x = sin x/cos x

    integral sinx/cos x dx

    let u = cos x
    du = -sin x dx
    - du = sin x dx

    integral: -(1/u) du

    = ln u = -ln cos x

    but sec x = 1/cos x

    ...?

    Edit:

    Nvm figured it out -.-

    - ln cos x = ln cos x^-1
    = ln sec x

    so they are equivalent....duh
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  2. #2
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    There is nothing wrong with your mathematics, so your book must be wrong: integral tanx dx - Wolfram|Alpha

    Looks like you are right.
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  3. #3
    MHF Contributor

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    The book is saying the same thing he is and the same thing Wolfram is:
    -ln|cos(x)|= ln|\frac{1}{cos(x)}|= ln|sec(x)|
    (Plus a constant, of course.)
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