Integraal van $$$\frac{75 i d n t x^{32}}{p^{2}}$$$ met betrekking tot $$$x$$$

Bepaal $$$\int \frac{75 i d n t x^{32}}{p^{2}}\, dx$$$.

Pas de constante-veelvoudregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ toe met $$$c=\frac{75 i d n t}{p^{2}}$$$ en $$$f{\left(x \right)} = x^{32}$$$:

$${\color{red}{\int{\frac{75 i d n t x^{32}}{p^{2}} d x}}} = {\color{red}{\left(\frac{75 i d n t \int{x^{32} d x}}{p^{2}}\right)}}$$

Pas de machtsregel $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ toe met $$$n=32$$$:

$$\frac{75 i d n t {\color{red}{\int{x^{32} d x}}}}{p^{2}}=\frac{75 i d n t {\color{red}{\frac{x^{1 + 32}}{1 + 32}}}}{p^{2}}=\frac{75 i d n t {\color{red}{\left(\frac{x^{33}}{33}\right)}}}{p^{2}}$$

Dus,

$$\int{\frac{75 i d n t x^{32}}{p^{2}} d x} = \frac{25 i d n t x^{33}}{11 p^{2}}$$

Voeg de integratieconstante toe:

$$\int{\frac{75 i d n t x^{32}}{p^{2}} d x} = \frac{25 i d n t x^{33}}{11 p^{2}}+C$$

$$$\int \frac{75 i d n t x^{32}}{p^{2}}\, dx = \frac{25 i d n t x^{33}}{11 p^{2}} + C$$$A