Integraal van $$$\frac{3}{14641 x^{2}}$$$

Bepaal $$$\int \frac{3}{14641 x^{2}}\, dx$$$.

Pas de constante-veelvoudregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ toe met $$$c=\frac{3}{14641}$$$ en $$$f{\left(x \right)} = \frac{1}{x^{2}}$$$:

$${\color{red}{\int{\frac{3}{14641 x^{2}} d x}}} = {\color{red}{\left(\frac{3 \int{\frac{1}{x^{2}} d x}}{14641}\right)}}$$

Pas de machtsregel $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ toe met $$$n=-2$$$:

$$\frac{3 {\color{red}{\int{\frac{1}{x^{2}} d x}}}}{14641}=\frac{3 {\color{red}{\int{x^{-2} d x}}}}{14641}=\frac{3 {\color{red}{\frac{x^{-2 + 1}}{-2 + 1}}}}{14641}=\frac{3 {\color{red}{\left(- x^{-1}\right)}}}{14641}=\frac{3 {\color{red}{\left(- \frac{1}{x}\right)}}}{14641}$$

Dus,

$$\int{\frac{3}{14641 x^{2}} d x} = - \frac{3}{14641 x}$$

Voeg de integratieconstante toe:

$$\int{\frac{3}{14641 x^{2}} d x} = - \frac{3}{14641 x}+C$$

$$$\int \frac{3}{14641 x^{2}}\, dx = - \frac{3}{14641 x} + C$$$A