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Math Help - Integration using given substitution difficulty.

  1. #1
    Member Furyan's Avatar
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    Integration using given substitution difficulty.

    Hello again,

    Just when I think I'm getting it I realize I'm really not.

    I have no idea how to approach this question, I have a bunch like this to do and would really appreciate some help.

    The question is, using the substitution:

    u^2 = 1 + \tan(x)

    Evaluate the integral:

    \int\sec^2(x)\tan(x)\sqrt{1 + \tan(x)} dx

    I know that:

     \tan(x) = u^2 - 1 that  \sec^2(x) = \tan^2(x) + 1 and that u = \sqrt{1 + \tan(x)} but have no idea how to proceed. I have looked in all my text books but can't't find an example similar enough to help me figure out what to do.

    Thank you.
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  2. #2
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    Re: Integration using given substitution difficulty.

    Use implicit differentiation to find du/dx
    From
    u^2 = 1 + \tan(x)
    2u du/dx = \sec^2(x)

    Replace
    \sec^2(x) dx with 2u du
    And replace \tan(x) with u^2 -1
    Thanks from Furyan
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