Answer
$$1+\ln (\ln x)$$
Work Step by Step
The solution of the given form is: $y(x)=y_0+\int_{x_0}^x f(t) \ dt $
We have: $y(x)=1+\int_{e}^{x} \dfrac{1}{t \ln t} \ dt$
Let us consider that $a=\ln t \implies da=\dfrac{dt}{t}$
Now, $y(x)=1+\int_{1}^{\ln (x)} \dfrac{1}{a} \ da \\=1+|\ln a|_1^{\ln x}\\=1+\ln (\ln x)$
