To evaluate the integral of ( \frac{\ln(x)}{x^2} ), we can utilize the method of integration by parts. The integral can be expressed as follows:

We choose our variables for integration by parts:

• Let ( u = \ln(x) ), which implies ( du = \frac{1}{x} , dx ).
• Let ( dv = \frac{1}{x^2} , dx ), which gives us ( v = -\frac{1}{x} ).

Applying the integration by parts formula, which is given by

we can substitute our choices into the formula:

The integral ( \int -\frac{1}{x} , dx ) can be evaluated using the standard rule for the integral of ( \frac{1}{x} ):

Now substituting this back into our previous expression, we have:

Next, we can simplify the expression:

Thus, the final result for the integral is:

In summary, the integral of ( \frac{\ln(x)}{x^2} ) is: