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Math Help - Improper Integral

  1. #1
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    Improper Integral

    integral (from 0 to infinity) of dx/rootx(x+1)
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  2. #2
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    When x is large, the integrand is approximately 1/x, so the integral will diverge.

    If that explanation isn't rigorous enought for you, you can integrate \int\frac{dx}{\sqrt{x(x+1)}} = \int\frac{2dx}{\sqrt{(2x+1)^2-1}} by making the substitution 2x+1=\sec\theta.
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