Determining when an integral converges or diverges

genu

1. The problem statement, all variables and given/known data
determine whether the integral converges or diverges:
[tex]\int_0^1\!\sqrt{\frac{(1+x)}{(1-x)}}dx[/tex]

2. Relevant equations

I know what if the value is a finite number, it converges, otherwise it diverges. Teacher was was able to determine the fact just by looking at it... what is the procedure for this?

Dick

You look near the point where the integrand is singular, in this case near x=1. The numerator is ~2 and the denominator (1-x)=y is near zero. So the integral is going to have the same convergence properties as the integral of 1/sqrt(y) around zero. It converges.