Integraal van $$$i n t x^{42}$$$ met betrekking tot $$$x$$$

Bepaal $$$\int i n t x^{42}\, dx$$$.

Pas de constante-veelvoudregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ toe met $$$c=i n t$$$ en $$$f{\left(x \right)} = x^{42}$$$:

$${\color{red}{\int{i n t x^{42} d x}}} = {\color{red}{i n t \int{x^{42} d x}}}$$

Pas de machtsregel $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ toe met $$$n=42$$$:

$$i n t {\color{red}{\int{x^{42} d x}}}=i n t {\color{red}{\frac{x^{1 + 42}}{1 + 42}}}=i n t {\color{red}{\left(\frac{x^{43}}{43}\right)}}$$

Dus,

$$\int{i n t x^{42} d x} = \frac{i n t x^{43}}{43}$$

Voeg de integratieconstante toe:

$$\int{i n t x^{42} d x} = \frac{i n t x^{43}}{43}+C$$

$$$\int i n t x^{42}\, dx = \frac{i n t x^{43}}{43} + C$$$A