Questions: Calculate the integral and write the answer in simplest form. [ intleft(5-x^-2right) d x ]

Solution Steps

To solve the integral \(\int\left(5-x^{-2}\right) dx\), we need to integrate each term separately. The integral of a constant is the constant times the variable, and the integral of \(x^{-2}\) can be found using the power rule for integration.

We start with the integral to be solved: \[ \int\left(5 - x^{-2}\right) dx \]

We can integrate each term separately:

1. The integral of \(5\) is \(5x\).
2. The integral of \(-x^{-2}\) is \(\frac{1}{x}\) (using the power rule).

Thus, we have: \[ \int\left(5 - x^{-2}\right) dx = 5x + \frac{1}{x} + C \] where \(C\) is the constant of integration.

The result of the integration is already in its simplest form: \[ 5x + \frac{1}{x} + C \]

Final Answer