Integral dari $$$j_{0} x^{5}$$$ terhadap $$$x$$$

Temukan $$$\int j_{0} x^{5}\, dx$$$.

Terapkan aturan pengali konstanta $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ dengan $$$c=j_{0}$$$ dan $$$f{\left(x \right)} = x^{5}$$$:

$${\color{red}{\int{j_{0} x^{5} d x}}} = {\color{red}{j_{0} \int{x^{5} d x}}}$$

Terapkan aturan pangkat $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ dengan $$$n=5$$$:

$$j_{0} {\color{red}{\int{x^{5} d x}}}=j_{0} {\color{red}{\frac{x^{1 + 5}}{1 + 5}}}=j_{0} {\color{red}{\left(\frac{x^{6}}{6}\right)}}$$

Oleh karena itu,

$$\int{j_{0} x^{5} d x} = \frac{j_{0} x^{6}}{6}$$

Tambahkan konstanta integrasi:

$$\int{j_{0} x^{5} d x} = \frac{j_{0} x^{6}}{6}+C$$

$$$\int j_{0} x^{5}\, dx = \frac{j_{0} x^{6}}{6} + C$$$A