To solve the integral ∫ rac{1}{x^2} \, dx, we start by rewriting the integrand. The expression rac{1}{x^2} can be rewritten as x^{-2}.
Using the power rule for integration, we have:
- For any constant n, the integral ∫ x^n \, dx = rac{x^{n+1}}{n+1} + C, where C is the constant of integration.
In our case, n = -2. Applying the power rule:
∫ x^{-2} \, dx = rac{x^{-2 + 1}}{-2 + 1} + C = rac{x^{-1}}{-1} + C = - rac{1}{x} + C.
Thus, the final result for the integral is:
– rac{1}{x} + C