Determine the definite integral for y=x+1/x. x=1 and x=3

The definite integral is calculated using Leibniz-Newton
formula.

Int (x + 1/x)dx = F(b) - F(a), where a = 1 and b =
3

First, we'll determine the result of the indefinite
integral:

Int (x +
1/x)dx

We'll use the additive property of
integrals:

Int (x + 1/x)dx = Int xdx + Int
dx/x

Int (x + 1/x)dx = x^2/2 + ln x +
C

The resulted expression is
F(x).

Now, we'll determine F(b) = F(3) and F(a) =
F(1):

F(3) = 3^2/2 + ln 3

F(3)
= 9/2 + ln 3

F(1) = 1/2 + ln
1

F(1) = 1/2 + 0

F(1) =
1/2

We'll determine the definite
integral:

Int (x + 1/x)dx = F(3) -
F(1)

Int (x + 1/x)dx = 9/2 + ln 3 -
1/2

We'll combine like
terms:

Int (x + 1/x)dx = 4 + ln
3