Integral dari $$$\frac{y^{3}}{x^{4}}$$$ terhadap $$$x$$$

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

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

$${\color{red}{\int{\frac{y^{3}}{x^{4}} d x}}} = {\color{red}{y^{3} \int{\frac{1}{x^{4}} d x}}}$$

Terapkan aturan pangkat $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ dengan $$$n=-4$$$:

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

Oleh karena itu,

$$\int{\frac{y^{3}}{x^{4}} d x} = - \frac{y^{3}}{3 x^{3}}$$

Tambahkan konstanta integrasi:

$$\int{\frac{y^{3}}{x^{4}} d x} = - \frac{y^{3}}{3 x^{3}}+C$$

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