Integral de $$$\frac{4}{t^{2}}$$$

Encontre $$$\int \frac{4}{t^{2}}\, dt$$$.

Aplique a regra do múltiplo constante $$$\int c f{\left(t \right)}\, dt = c \int f{\left(t \right)}\, dt$$$ usando $$$c=4$$$ e $$$f{\left(t \right)} = \frac{1}{t^{2}}$$$:

$${\color{red}{\int{\frac{4}{t^{2}} d t}}} = {\color{red}{\left(4 \int{\frac{1}{t^{2}} d t}\right)}}$$

Aplique a regra da potência $$$\int t^{n}\, dt = \frac{t^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ com $$$n=-2$$$:

$$4 {\color{red}{\int{\frac{1}{t^{2}} d t}}}=4 {\color{red}{\int{t^{-2} d t}}}=4 {\color{red}{\frac{t^{-2 + 1}}{-2 + 1}}}=4 {\color{red}{\left(- t^{-1}\right)}}=4 {\color{red}{\left(- \frac{1}{t}\right)}}$$

Portanto,

$$\int{\frac{4}{t^{2}} d t} = - \frac{4}{t}$$

Adicione a constante de integração:

$$\int{\frac{4}{t^{2}} d t} = - \frac{4}{t}+C$$

$$$\int \frac{4}{t^{2}}\, dt = - \frac{4}{t} + C$$$A