Integral de $$$\frac{4}{t^{3}}$$$

Halla $$$\int \frac{4}{t^{3}}\, dt$$$.

Aplica la regla del factor constante $$$\int c f{\left(t \right)}\, dt = c \int f{\left(t \right)}\, dt$$$ con $$$c=4$$$ y $$$f{\left(t \right)} = \frac{1}{t^{3}}$$$:

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

Aplica la regla de la potencia $$$\int t^{n}\, dt = \frac{t^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ con $$$n=-3$$$:

$$4 {\color{red}{\int{\frac{1}{t^{3}} d t}}}=4 {\color{red}{\int{t^{-3} d t}}}=4 {\color{red}{\frac{t^{-3 + 1}}{-3 + 1}}}=4 {\color{red}{\left(- \frac{t^{-2}}{2}\right)}}=4 {\color{red}{\left(- \frac{1}{2 t^{2}}\right)}}$$

Por lo tanto,

$$\int{\frac{4}{t^{3}} d t} = - \frac{2}{t^{2}}$$

Añade la constante de integración:

$$\int{\frac{4}{t^{3}} d t} = - \frac{2}{t^{2}}+C$$

$$$\int \frac{4}{t^{3}}\, dt = - \frac{2}{t^{2}} + C$$$A