What is the antiderivative of $\frac{1}{{x}^{2}}$?

Answer & Explanation

Eugene Rich

Beginner2023-03-06Added 3 answers

You would apply the power rule for antiderivatives/integrals to this antiderivative. This states that $\int {x}^{n}=\frac{1}{n+1}\left({x}^{n+1}\right)$. Since $\frac{1}{{x}^{2}}={x}^{-2}$ and $n\ne -1$ in this case, you can apply this power rule. Answer: $\int \frac{1}{{x}^{2}}=\int {x}^{-2}=\frac{{x}^{-1}}{-1}+c=-\frac{1}{x}+c$