Integraal van $$$\frac{1}{10000 x^{4}}$$$

Bepaal $$$\int \frac{1}{10000 x^{4}}\, dx$$$.

Pas de constante-veelvoudregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ toe met $$$c=\frac{1}{10000}$$$ en $$$f{\left(x \right)} = \frac{1}{x^{4}}$$$:

$${\color{red}{\int{\frac{1}{10000 x^{4}} d x}}} = {\color{red}{\left(\frac{\int{\frac{1}{x^{4}} d x}}{10000}\right)}}$$

Pas de machtsregel $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ toe met $$$n=-4$$$:

$$\frac{{\color{red}{\int{\frac{1}{x^{4}} d x}}}}{10000}=\frac{{\color{red}{\int{x^{-4} d x}}}}{10000}=\frac{{\color{red}{\frac{x^{-4 + 1}}{-4 + 1}}}}{10000}=\frac{{\color{red}{\left(- \frac{x^{-3}}{3}\right)}}}{10000}=\frac{{\color{red}{\left(- \frac{1}{3 x^{3}}\right)}}}{10000}$$

Dus,

$$\int{\frac{1}{10000 x^{4}} d x} = - \frac{1}{30000 x^{3}}$$

Voeg de integratieconstante toe:

$$\int{\frac{1}{10000 x^{4}} d x} = - \frac{1}{30000 x^{3}}+C$$

$$$\int \frac{1}{10000 x^{4}}\, dx = - \frac{1}{30000 x^{3}} + C$$$A