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Math Help - integration by reciprocal subsitution

  1. #1
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    integration by reciprocal subsitution

    integrate dx/ sqrt (x^2 - x + 1) throughb reciprocal substitution

    i tried solving but i was stuck in
    du / u x sqrt (1-u+u ^2)

    u = 1/x
    Last edited by sean123; February 9th 2010 at 04:55 AM.
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  2. #2
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    Quote Originally Posted by sean123 View Post
    integrate dx/ sqrt (x^2 - x + 1) throughb reciprocal substitution

    i tried solving but i was stuck in
    du / u x sqrt (1-u+u ^2)

    u = 1/x
    Dear sean,

    \int{\frac{dx}{\sqrt{x^{2}-x+1}}}

    \int{\frac{dx}{\sqrt{\left(x-\frac{1}{2}\right)^{2}-\frac{1}{4}+1}}}

    \int{\frac{dx}{\sqrt{\left(x-\frac{1}{2}\right)^{2}+\frac{3}{4}}}}

    Now substitute x-\frac{1}{2}=\frac{\sqrt3}{2}tanU

    See if you can do it from here. If you need more assistance please don't hesitate to reply me.
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