Question

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

Answer 1

**the "S" is the integral sign

Answer 2

**the "S" is the integral sign

Answer 3

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