[Math] integral of 1/(sqrt(e^x)) from 0 to infinity(Improper integral)

Question

I'm taking Calculus 1 course and I'm having problems with the following integrals(Improper integrals)

1. $\displaystyle\int_0^{\infty} \frac1{\sqrt{e^x}}$ dx
2. $\displaystyle\int_0^1 e^\frac1x$ dx
3. $\displaystyle\int_1^\infty (1+\sin x)\cdot e^{-x}$ dx

Answer for third:

$\displaystyle\int_1^\infty (1+\sin x)\cdot e^{-x}$ dx < $\displaystyle\int_1^\infty (2)\cdot e^{-x}$ dx = 1

Therefor it be can bounded

Thanks for your help-(helpful sites will also be appriciated)

Answer 1

HINT for 1:

$\displaystyle \frac1{\sqrt{e^x}}=\frac1{(e^x)^\frac12}=e^{-\frac12x}$