We know that fx 0intxeet dt is a continuous function by

Question

We know that F(x) = ₀∫^xe^{e^t} dt is a continuous function by FTC1, though it is not an elementary function. The functions

∫(e^x/x) dx and ∫(1/In x) dx

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

a. ₁∫²(e^x/x) dx;        b. ₂∫³(1/In x) dx