Integral von $$$\frac{1}{n^{11}}$$$

Bestimme $$$\int \frac{1}{n^{11}}\, dn$$$.

Wenden Sie die Potenzregel $$$\int n^{n}\, dn = \frac{n^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ mit $$$n=-11$$$ an:

$${\color{red}{\int{\frac{1}{n^{11}} d n}}}={\color{red}{\int{n^{-11} d n}}}={\color{red}{\frac{n^{-11 + 1}}{-11 + 1}}}={\color{red}{\left(- \frac{n^{-10}}{10}\right)}}={\color{red}{\left(- \frac{1}{10 n^{10}}\right)}}$$

Daher,

$$\int{\frac{1}{n^{11}} d n} = - \frac{1}{10 n^{10}}$$

Fügen Sie die Integrationskonstante hinzu:

$$\int{\frac{1}{n^{11}} d n} = - \frac{1}{10 n^{10}}+C$$

$$$\int \frac{1}{n^{11}}\, dn = - \frac{1}{10 n^{10}} + C$$$A