We know that $ F(x) = \displaystyle \int_0^x e^{e^t}\ dt $ is a continuous function by FTC1, though it is not an elementary function. The functions
$ \displaystyle \int \frac{e^x}{x}\ dx $ and $ \displaystyle \int \frac{1}{\ln x}\ dx $
are not elementary either, but they can be expressed in terms of $ F $. Evaluate the following integrals in terms of $ F $.
$ \displaystyle \int_1^2 \frac{e^x}{x}\ dx $ and $ \displaystyle \int_2^3 \frac{1}{\ln x}\ dx $