Integralen av $$$x^{\frac{21}{10}}$$$

Bestäm $$$\int x^{\frac{21}{10}}\, dx$$$.

Tillämpa potensregeln $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ med $$$n=\frac{21}{10}$$$:

$${\color{red}{\int{x^{\frac{21}{10}} d x}}}={\color{red}{\frac{x^{1 + \frac{21}{10}}}{1 + \frac{21}{10}}}}={\color{red}{\left(\frac{10 x^{\frac{31}{10}}}{31}\right)}}$$

Alltså,

$$\int{x^{\frac{21}{10}} d x} = \frac{10 x^{\frac{31}{10}}}{31}$$

Lägg till integrationskonstanten:

$$\int{x^{\frac{21}{10}} d x} = \frac{10 x^{\frac{31}{10}}}{31}+C$$

$$$\int x^{\frac{21}{10}}\, dx = \frac{10 x^{\frac{31}{10}}}{31} + C$$$A