What is the integrant for the function e^x+1/x ?

The integrand is the result of differentiation of F(x),
namely the function f(x).

Int f(x) dx =
F(x)

or

F'(x) =
f(x)

Since the integral of f(x) is e^x + 1/x, then we have
to differentiate the result to determine the expression
of f(x).

So, we'll compute the first derivative of the
expression resulted after we've integrated f(x).

We'll note
the result as F(x) =  e^x + 1/x

F'(x) = ( e^x +
1/x)'

F'(x) = (e^x)' +
(1/x)'

We'll compute the first derivative of (1/x) applying
the quotients rule:

(f/g)' = (f'*g -
f*g')/g^2

(1/x) = (1'*x -
1*x')/x^2

(1/x) = (0 -
1)/x^2

(1/x) = -1/x^2

F'(x)
= e^x - 1/x^2

But F'(x) =
f(x)

So, f(x) = e^x -
1/x^2