Integralen av $$$x^{\frac{7}{6}}$$$

Bestäm $$$\int x^{\frac{7}{6}}\, dx$$$.

Tillämpa potensregeln $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ med $$$n=\frac{7}{6}$$$:

$${\color{red}{\int{x^{\frac{7}{6}} d x}}}={\color{red}{\frac{x^{1 + \frac{7}{6}}}{1 + \frac{7}{6}}}}={\color{red}{\left(\frac{6 x^{\frac{13}{6}}}{13}\right)}}$$

Alltså,

$$\int{x^{\frac{7}{6}} d x} = \frac{6 x^{\frac{13}{6}}}{13}$$

Lägg till integrationskonstanten:

$$\int{x^{\frac{7}{6}} d x} = \frac{6 x^{\frac{13}{6}}}{13}+C$$

$$$\int x^{\frac{7}{6}}\, dx = \frac{6 x^{\frac{13}{6}}}{13} + C$$$A