Argue that the integral

${\displaystyle \underset{1}{\overset{}{}}}\frac{du}{u+u^2}$

converges by using a comparison. Then use partial fractions to find the value to which it converges.

$5.$ Argue that the integral

${\displaystyle \underset{0}{\overset{}{}}}\frac{dy}{1+e^y}$

converges by using a comparison. Then use a substitution to find the value to which it converges.