|
|
|
|
|
|
|
|
|
|
|
|
Integraal van $$$\frac{1}{\sqrt[6]{x}}$$$
Gerelateerde rekenmachine: Rekenmachine voor bepaalde en oneigenlijke integralen
Uw invoer
Bepaal $$$\int \frac{1}{\sqrt[6]{x}}\, dx$$$.
Oplossing
Pas de machtsregel $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ toe met $$$n=- \frac{1}{6}$$$:
$${\color{red}{\int{\frac{1}{\sqrt[6]{x}} d x}}}={\color{red}{\int{x^{- \frac{1}{6}} d x}}}={\color{red}{\frac{x^{- \frac{1}{6} + 1}}{- \frac{1}{6} + 1}}}={\color{red}{\left(\frac{6 x^{\frac{5}{6}}}{5}\right)}}$$
Dus,
$$\int{\frac{1}{\sqrt[6]{x}} d x} = \frac{6 x^{\frac{5}{6}}}{5}$$
Voeg de integratieconstante toe:
$$\int{\frac{1}{\sqrt[6]{x}} d x} = \frac{6 x^{\frac{5}{6}}}{5}+C$$
Antwoord
$$$\int \frac{1}{\sqrt[6]{x}}\, dx = \frac{6 x^{\frac{5}{6}}}{5} + C$$$A