Is the number $$\int_1^2 \frac{e^x} x \, dx=Ei(2)-Ei(1)$$ transcendental ?
The first few digits are
$$3.059116539645953407912984195895401006500992980687334462880866822688\cdots$$
Working with lindep and algdep-command with PARI/GP I did not find an indicitation that the given number is algebraic. But can it be proven that it is transcendental ?
I tried to apply the known powerful theorems (Lindemann-Weierstrass and Baker ), but without success.
If the number cannot be verified, is at least the status of $Ei(1)$ and $Ei(2)$ known ?
Here
https://en.wikipedia.org/wiki/Exponential_integral
the definition of $Ei(x)$