Integraal van $$$- 30229 x^{6} y^{9} z^{5}$$$ met betrekking tot $$$x$$$

Bepaal $$$\int \left(- 30229 x^{6} y^{9} z^{5}\right)\, dx$$$.

Pas de constante-veelvoudregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ toe met $$$c=- 30229 y^{9} z^{5}$$$ en $$$f{\left(x \right)} = x^{6}$$$:

$${\color{red}{\int{\left(- 30229 x^{6} y^{9} z^{5}\right)d x}}} = {\color{red}{\left(- 30229 y^{9} z^{5} \int{x^{6} d x}\right)}}$$

Pas de machtsregel $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ toe met $$$n=6$$$:

$$- 30229 y^{9} z^{5} {\color{red}{\int{x^{6} d x}}}=- 30229 y^{9} z^{5} {\color{red}{\frac{x^{1 + 6}}{1 + 6}}}=- 30229 y^{9} z^{5} {\color{red}{\left(\frac{x^{7}}{7}\right)}}$$

Dus,

$$\int{\left(- 30229 x^{6} y^{9} z^{5}\right)d x} = - \frac{30229 x^{7} y^{9} z^{5}}{7}$$

Voeg de integratieconstante toe:

$$\int{\left(- 30229 x^{6} y^{9} z^{5}\right)d x} = - \frac{30229 x^{7} y^{9} z^{5}}{7}+C$$

$$$\int \left(- 30229 x^{6} y^{9} z^{5}\right)\, dx = - \frac{30229 x^{7} y^{9} z^{5}}{7} + C$$$A