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Math Help - Trouble with integration (trig. inverse forms)

  1. #1
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    Trouble with integration (trig. inverse forms)

    Here is the link from wolframalpha:
    integral (1/[(e^(4x) -36)^(1/2)])dx - Wolfram|Alpha

    I understand what W.A. did, but i think there should be an easier way than making so many substitutions.
    I would appreciate hints, don't solve it entirely.

    Thanks.
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  2. #2
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    Quote Originally Posted by Arturo_026 View Post
    Here is the link from wolframalpha:
    integral (1/[(e^(4x) -36)^(1/2)])dx - Wolfram|Alpha

    I understand what W.A. did, but i think there should be an easier way than making so many substitutions.
    I would appreciate hints, don't solve it entirely.
    Since the denominator is of the form

    \sqrt{y^2-6^2}

    This suggests the trig sub y=6\sec{t} but y=e^{2x} so you get

    e^{2x}=6\sec{t}

    This will combine all the substituions that WA did into one step
    Thanks.
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  3. #3
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    Thanks, but I haven't been thought that or seen a similar method. This problem is from a chapter on inverse trigonometric and hyperbolic functions. (or perhaps just inverses, logs, and exponoential).
    -Thanks
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  4. #4
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    I finally figured it out.!!! By timing top and bottom by e^(2x) i get the sec inverse form.
    Thanks for the help
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