Integrate: int (x^-3)/(3)dx=

To integrate the given expression, we can use the power rule for integration. The power rule states that the integral of \(x^n\) with respect to \(x\) is \(\frac{x^{n+1}}{n+1} + C\), where \(C\) is the constant of integration.<br /><br />Given:<br />\[<br />\int \frac{x^{-3}}{3} \, dx<br />\]<br /><br />We can rewrite the integrand as:<br />\[<br />\frac{1}{3} \int x^{-3} \, dx<br />\]<br /><br />Now, apply the power rule:<br />\[<br />\frac{1}{3} \cdot \frac{x^{-3+1}}{-3+1} + C = \frac{1}{3} \cdot \frac{x^{-2}}{-2} + C<br />\]<br /><br />Simplify the expression:<br />\[<br />\frac{1}{3} \cdot \left(-\frac{1}{2}\right) x^{-2} + C = -\frac{1}{6} x^{-2} + C<br />\]<br /><br />So, the integral is:<br />\[<br />\int \frac{x^{-3}}{3} \, dx = -\frac{1}{6} x^{-2} + C<br />\]