Integralen av $$$\frac{1}{x^{14}}$$$

Bestäm $$$\int \frac{1}{x^{14}}\, dx$$$.

Tillämpa potensregeln $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ med $$$n=-14$$$:

$${\color{red}{\int{\frac{1}{x^{14}} d x}}}={\color{red}{\int{x^{-14} d x}}}={\color{red}{\frac{x^{-14 + 1}}{-14 + 1}}}={\color{red}{\left(- \frac{x^{-13}}{13}\right)}}={\color{red}{\left(- \frac{1}{13 x^{13}}\right)}}$$

Alltså,

$$\int{\frac{1}{x^{14}} d x} = - \frac{1}{13 x^{13}}$$

Lägg till integrationskonstanten:

$$\int{\frac{1}{x^{14}} d x} = - \frac{1}{13 x^{13}}+C$$

$$$\int \frac{1}{x^{14}}\, dx = - \frac{1}{13 x^{13}} + C$$$A