The given function is \(\frac{1 - x}{x^3}\). We can split this into two separate fractions as follows:

\(\frac{1 - x}{x^3} = \frac{1}{x^3} - \frac{x}{x^3} = \frac{1}{x^3} - \frac{1}{x^2}\)

Now, we can integrate each term separately with respect to x. The antiderivative of \(\frac{1}{x^n}\) is \(-\frac{1}{(n-1)x^{n-1}} + C\), where C is the constant of integration. Applying this rule to each term, we get:

\(\int (\frac{1}{x^3} - \frac{1}{x^2}) dx = -\frac{1}{2x^2} + \frac{1}{x} + k\)

where k is the constant of integration.