Exponential integral question How would I solve the following problem?
$$f(x)=\int\!\frac{4}{\sqrt{e^x}}\,dx$$
Using $u$ substitution I have set $u=e^x$ andd $du=e^x dx$
so would I have $$4\int\!\frac{du}{\sqrt{u}}$$
What would I do from here?

Stop!  Use law of exponents:
$$\sqrt{e^x} = e^{x/2}$$
Better yet:
$$\frac{1}{\sqrt{e^x}} = e^{-x/2}$$
By the way, using your method, you should have a factor of $1/u^{3/2}$ in the integral.
