Integral of $$$\frac{1}{x^{70}}$$$

Find $$$\int \frac{1}{x^{70}}\, dx$$$.

Apply the power rule $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=-70$$$:

$${\color{red}{\int{\frac{1}{x^{70}} d x}}}={\color{red}{\int{x^{-70} d x}}}={\color{red}{\frac{x^{-70 + 1}}{-70 + 1}}}={\color{red}{\left(- \frac{x^{-69}}{69}\right)}}={\color{red}{\left(- \frac{1}{69 x^{69}}\right)}}$$

Therefore,

$$\int{\frac{1}{x^{70}} d x} = - \frac{1}{69 x^{69}}$$

Add the constant of integration:

$$\int{\frac{1}{x^{70}} d x} = - \frac{1}{69 x^{69}}+C$$

$$$\int \frac{1}{x^{70}}\, dx = - \frac{1}{69 x^{69}} + C$$$A