|
|
|
|
|
|
|
|
|
|
|
|
Integraal van $$$\frac{13}{x^{\frac{28}{5}}}$$$
Gerelateerde rekenmachine: Rekenmachine voor bepaalde en oneigenlijke integralen
Uw invoer
Bepaal $$$\int \frac{13}{x^{\frac{28}{5}}}\, dx$$$.
Oplossing
Pas de constante-veelvoudregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ toe met $$$c=13$$$ en $$$f{\left(x \right)} = \frac{1}{x^{\frac{28}{5}}}$$$:
$${\color{red}{\int{\frac{13}{x^{\frac{28}{5}}} d x}}} = {\color{red}{\left(13 \int{\frac{1}{x^{\frac{28}{5}}} d x}\right)}}$$
Pas de machtsregel $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ toe met $$$n=- \frac{28}{5}$$$:
$$13 {\color{red}{\int{\frac{1}{x^{\frac{28}{5}}} d x}}}=13 {\color{red}{\int{x^{- \frac{28}{5}} d x}}}=13 {\color{red}{\frac{x^{- \frac{28}{5} + 1}}{- \frac{28}{5} + 1}}}=13 {\color{red}{\left(- \frac{5 x^{- \frac{23}{5}}}{23}\right)}}=13 {\color{red}{\left(- \frac{5}{23 x^{\frac{23}{5}}}\right)}}$$
Dus,
$$\int{\frac{13}{x^{\frac{28}{5}}} d x} = - \frac{65}{23 x^{\frac{23}{5}}}$$
Voeg de integratieconstante toe:
$$\int{\frac{13}{x^{\frac{28}{5}}} d x} = - \frac{65}{23 x^{\frac{23}{5}}}+C$$
Antwoord
$$$\int \frac{13}{x^{\frac{28}{5}}}\, dx = - \frac{65}{23 x^{\frac{23}{5}}} + C$$$A