anonymous 5 years ago hi i need to determine whether the following improper integral is convergent or divergent and determine it's value S b=infinity a=0 (e^x)/(e^e^x) dx

1. anonymous

**the "S" is the integral sign

2. anonymous

**the "S" is the integral sign

3. nikvist

$y=e^{e^x},\ln y=e^x,\frac{y'}{y}=e^x,\frac{dy}{y}=e^xdx$ $\int\limits_0^{+\infty}\frac{e^x}{e^{e^x}}dx= \int\limits_e^{+\infty}\frac{dy/y}{y}=\left(-\frac{1}{y}\right)_e^{+\infty}=\frac{1}{e}$