Integral de $$$\frac{3}{t^{10}}$$$

Encontre $$$\int \frac{3}{t^{10}}\, dt$$$.

Aplique a regra do múltiplo constante $$$\int c f{\left(t \right)}\, dt = c \int f{\left(t \right)}\, dt$$$ usando $$$c=3$$$ e $$$f{\left(t \right)} = \frac{1}{t^{10}}$$$:

$${\color{red}{\int{\frac{3}{t^{10}} d t}}} = {\color{red}{\left(3 \int{\frac{1}{t^{10}} d t}\right)}}$$

Aplique a regra da potência $$$\int t^{n}\, dt = \frac{t^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ com $$$n=-10$$$:

$$3 {\color{red}{\int{\frac{1}{t^{10}} d t}}}=3 {\color{red}{\int{t^{-10} d t}}}=3 {\color{red}{\frac{t^{-10 + 1}}{-10 + 1}}}=3 {\color{red}{\left(- \frac{t^{-9}}{9}\right)}}=3 {\color{red}{\left(- \frac{1}{9 t^{9}}\right)}}$$

Portanto,

$$\int{\frac{3}{t^{10}} d t} = - \frac{1}{3 t^{9}}$$

Adicione a constante de integração:

$$\int{\frac{3}{t^{10}} d t} = - \frac{1}{3 t^{9}}+C$$

$$$\int \frac{3}{t^{10}}\, dt = - \frac{1}{3 t^{9}} + C$$$A