Integralen av $$$\frac{1}{x^{20}}$$$

Bestäm $$$\int \frac{1}{x^{20}}\, dx$$$.

Tillämpa potensregeln $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ med $$$n=-20$$$:

$${\color{red}{\int{\frac{1}{x^{20}} d x}}}={\color{red}{\int{x^{-20} d x}}}={\color{red}{\frac{x^{-20 + 1}}{-20 + 1}}}={\color{red}{\left(- \frac{x^{-19}}{19}\right)}}={\color{red}{\left(- \frac{1}{19 x^{19}}\right)}}$$

Alltså,

$$\int{\frac{1}{x^{20}} d x} = - \frac{1}{19 x^{19}}$$

Lägg till integrationskonstanten:

$$\int{\frac{1}{x^{20}} d x} = - \frac{1}{19 x^{19}}+C$$

$$$\int \frac{1}{x^{20}}\, dx = - \frac{1}{19 x^{19}} + C$$$A