Integral dari $$$\frac{3}{4 x^{6}}$$$

Temukan $$$\int \frac{3}{4 x^{6}}\, dx$$$.

Terapkan aturan pengali konstanta $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ dengan $$$c=\frac{3}{4}$$$ dan $$$f{\left(x \right)} = \frac{1}{x^{6}}$$$:

$${\color{red}{\int{\frac{3}{4 x^{6}} d x}}} = {\color{red}{\left(\frac{3 \int{\frac{1}{x^{6}} d x}}{4}\right)}}$$

Terapkan aturan pangkat $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ dengan $$$n=-6$$$:

$$\frac{3 {\color{red}{\int{\frac{1}{x^{6}} d x}}}}{4}=\frac{3 {\color{red}{\int{x^{-6} d x}}}}{4}=\frac{3 {\color{red}{\frac{x^{-6 + 1}}{-6 + 1}}}}{4}=\frac{3 {\color{red}{\left(- \frac{x^{-5}}{5}\right)}}}{4}=\frac{3 {\color{red}{\left(- \frac{1}{5 x^{5}}\right)}}}{4}$$

Oleh karena itu,

$$\int{\frac{3}{4 x^{6}} d x} = - \frac{3}{20 x^{5}}$$

Tambahkan konstanta integrasi:

$$\int{\frac{3}{4 x^{6}} d x} = - \frac{3}{20 x^{5}}+C$$

$$$\int \frac{3}{4 x^{6}}\, dx = - \frac{3}{20 x^{5}} + C$$$A