Textbook Problem

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

${\displaystyle \int \frac{e^x}{x}}dx\text{and}{\displaystyle \int \frac{1}{\ln x}}dx$

are not elementary either, but they can be expressed in terms of F. Evaluate the following integrals in terms of F.

(a) ${\displaystyle {\int }_1^2\frac{e^x}{x}}dx$

(b) ${\displaystyle {\int }_2^3\frac{1}{\ln x}}dx$