Question

How do you integrate $\int \frac{1}{x^2}dx$.

Answer 1

Evaluate the integration:

The given integration is,

$\int \frac{1}{x^2}dx=\int x^{-2}dx$

$=\frac{x^{-2+1}}{-2+1}+c$ $\left[\because \int x^{n}dx=\frac{x^{n+1}}{n+1}\right]$

$=-x^{-1}+c$

$=-\frac{1}{x}+c$ $\left[\text{c be the integration constant}\right]$

Hence, the required answer is $\mathbf{-}\frac{\mathbf{1}}{\mathbf{x}}\mathbf{+}\mathit{c}$.