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Math Help - Having trouble with a Calculs Integration

  1. #1
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    Quebec
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    Unhappy Having trouble with a Calculs Integration

    The integration is [dx / (x Sqrt[1 - x])

    Seems pretty simple but the question specify to not use the Tanh integration formula...

    Now i'm stuck if my calculation are correct. Using the Pythagore i get to a point where i integrate Sec (theta)

    and stuck... got Ln sec (theta) + Tan (theta) + c... then nothing i can't find the right answer that fit with the real anwer that is

    If anyone could tell me if i made a mistake or send me in the right direction would be great


    Log[1 - Sqrt[1 - x]] - Log[1 + Sqrt[1 - x]]
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  2. #2
    MHF Contributor MarkFL's Avatar
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    St. Augustine, FL.
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    Re: Having trouble with a Calculs Integration

    If you observe that:

    x=(1+\sqrt{1-x})(1-\sqrt{1-x})

    and then make the substitution:

    u^2=1-x\,\therefore\,dx=-2u\,du

    you get:

    2\int\frac{du}{u^2-1}

    and now factor the denominator, and use partial fractions...
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  3. #3
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    Re: Having trouble with a Calculs Integration

    Wow fast answer and right answer just did the whole thing it work very well!!!

    Sorry if the problem was to easy I tought I'd put more of a challenge!

    Thanks MarkFl
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