Question

When evaluating the indefinite integral from 1 to infinity of x^2/(x+1)^2, can I take the square root of the numerator and denominator, since the integral only includes positive values? If not, what method should I use in order to go about evaluating this integral?

Answer 1

since the numerator and denominator both have the same degree, it is not likely that this integral will be finite

Answer 2

in fact you can be sure that it is not because the limit as x goes to infinity of the integrand is 1, so it doesn't even go to zero

Answer 3

Okay, I tried evaluating it using integration by parts and came to the same conclusion. Thank you.