What is the result of the integral ∫ (1/x^2) dx?

The integral of ( \frac{1}{x^2} ) can be solved using the power rule of integration. First, we rewrite ( \frac{1}{x^2} ) as ( x^{-2} ).

Now, applying the power rule for integration, which states that:

[

\int x^n , dx = \frac{x^{n+1}}{n+1} + C \quad \text{for } n \neq -1,

]

we can substitute ( n = -2 ) into this formula. Therefore, we have:

1. Increment the exponent: (-2 + 1 = -1).

2. Divide by the new exponent:

[

\frac{x^{-1}}{-1} = -\frac{1}{x}.

]

Thus, the result of the integral becomes:

[

\int \frac{1}{x^2} , dx = -\frac{1}{x} + C.

]

This confirms that the correct answer is the expression (-\frac{1}{x} + C).

The other options, while they might represent different functions, do not yield the correct outcome