Step 1a

We can rewrite the integrand as:

\$ (2x + 1) / x^2 = 2x/x^2 + 1/x^2 = 2/x + 1/x^2 \$

Splitting the integral, we get:

\$ \int 2/x dx + \int 1/x^2 dx \$

Explanation: Here, we rewrote and split the integrand.

Step 1b

The integration formulas are:

\$ \int 1/x dx = ln| x | + c , \int x^n dx = (x^(n+1)) /(n+1) + c \$

Now applying the formulas we get:

\$ 2 \int (1/x) dx + \int (x^(-2) ) dx \$

After integration, we get:

\$ 2 ln| x | + (x^(-2 + 1))/(-2+1) + c \$

After simplification :

\$ 2ln| x | + (x^(-1))/(-1) + c \$

\$ 2ln| x | - 1/x + c \$

Explanation: Here, after applied the formulas then we get \$ 2ln| x | - 1/x + c \$