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Math Help - complicated integral

  1. #1
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    complicated integral

    Compute the following integral

    \int_{-\infty}^{\infty} \frac{x-1}{x^3-1}dx


    The book says this is equal to \frac{2\pi}{\sqrt{3}}. However, I am not getting this answer. I keep getting different answers. How do I evaluate this integral?
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  2. #2
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    Quote Originally Posted by eskimo343 View Post
    Compute the following integral

    \int_{-\infty}^{\infty} \frac{x-1}{x^3-1}dx


    The book says this is equal to \frac{2\pi}{\sqrt{3}}. However, I am not getting this answer. I keep getting different answers. How do I evaluate this integral?
    Please show all your working. It will then be easier to help you.
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  3. #3
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    Quote Originally Posted by Chris L T521 View Post
    Factor first to get \int_{-\infty}^{\infty}\frac{x-1}{(x-1)(x^2+x+1)}\,dx=\int_{-\infty}^{\infty}\frac{\,dx}{x^2+x+1}.

    Since this is an even function, note that we can rewrite it as 2\int_0^{\infty}\frac{\,dx}{x^2+x+1}.

    Complete the square in the denominator, then integrate and simplify. Can you take it from here?
    Yes, I will try your suggestion.
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