Integral de $$$\frac{3}{y^{2}}$$$

Halla $$$\int \frac{3}{y^{2}}\, dy$$$.

Aplica la regla del factor constante $$$\int c f{\left(y \right)}\, dy = c \int f{\left(y \right)}\, dy$$$ con $$$c=3$$$ y $$$f{\left(y \right)} = \frac{1}{y^{2}}$$$:

$${\color{red}{\int{\frac{3}{y^{2}} d y}}} = {\color{red}{\left(3 \int{\frac{1}{y^{2}} d y}\right)}}$$

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

$$3 {\color{red}{\int{\frac{1}{y^{2}} d y}}}=3 {\color{red}{\int{y^{-2} d y}}}=3 {\color{red}{\frac{y^{-2 + 1}}{-2 + 1}}}=3 {\color{red}{\left(- y^{-1}\right)}}=3 {\color{red}{\left(- \frac{1}{y}\right)}}$$

Por lo tanto,

$$\int{\frac{3}{y^{2}} d y} = - \frac{3}{y}$$

Añade la constante de integración:

$$\int{\frac{3}{y^{2}} d y} = - \frac{3}{y}+C$$

$$$\int \frac{3}{y^{2}}\, dy = - \frac{3}{y} + C$$$A