Integral de $$$\frac{y}{x^{2}}$$$ con respecto a $$$x$$$

Halla $$$\int \frac{y}{x^{2}}\, dx$$$.

Aplica la regla del factor constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ con $$$c=y$$$ y $$$f{\left(x \right)} = \frac{1}{x^{2}}$$$:

$${\color{red}{\int{\frac{y}{x^{2}} d x}}} = {\color{red}{y \int{\frac{1}{x^{2}} d x}}}$$

Aplica la regla de la potencia $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ con $$$n=-2$$$:

$$y {\color{red}{\int{\frac{1}{x^{2}} d x}}}=y {\color{red}{\int{x^{-2} d x}}}=y {\color{red}{\frac{x^{-2 + 1}}{-2 + 1}}}=y {\color{red}{\left(- x^{-1}\right)}}=y {\color{red}{\left(- \frac{1}{x}\right)}}$$

Por lo tanto,

$$\int{\frac{y}{x^{2}} d x} = - \frac{y}{x}$$

Añade la constante de integración:

$$\int{\frac{y}{x^{2}} d x} = - \frac{y}{x}+C$$

$$$\int \frac{y}{x^{2}}\, dx = - \frac{y}{x} + C$$$A