# Math Help - Improper Integral

1. ## Improper Integral

integral (from 0 to infinity) of dx/rootx(x+1)

2. 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 $2x+1=\sec\theta$.