What is the area under the curve f(x) = (5+x^2)/x and x= 1 and x= 2

Given the curve f(x) = (5+ x^2 ) /
x 

We need to calculate the area between the curve f(x), x=
1, and x= 2.

We know that the area under the curve f(x) is
the integral of f(x).

Let F(x) = intg
f(x).

Then the area is:

A =
F(2) - F(1).......(1).

Let us determine the
integral.

F(x) = intg (5+ x^2 )/x 
dx

       = intg ( 5/x + x)
dx

       = intg (5/x) dx  + intg x
dx

       = 5*lnx + x^2
/2.

==> F(x) = 5lnx + x^2/2 +
C

==> F(2) = 5ln2 + 2 +
C.

==> F(1) = 5ln1 + 1/2 +
C

But we know that ln1 =
0.

==> F(1) = 1/2 +
C.

==> A = F(2) - F(1)
= 5ln2 + 2 - 1/2 = 5ln2 +
3/2

Then, the area between
f(x), x= 1,and x= 2 is:

A =
5ln2 + 3/2 square units.