Integral de $$$7 t^{\frac{3}{2}}$$$

Encontre $$$\int 7 t^{\frac{3}{2}}\, dt$$$.

Aplique a regra do múltiplo constante $$$\int c f{\left(t \right)}\, dt = c \int f{\left(t \right)}\, dt$$$ usando $$$c=7$$$ e $$$f{\left(t \right)} = t^{\frac{3}{2}}$$$:

$${\color{red}{\int{7 t^{\frac{3}{2}} d t}}} = {\color{red}{\left(7 \int{t^{\frac{3}{2}} d t}\right)}}$$

Aplique a regra da potência $$$\int t^{n}\, dt = \frac{t^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ com $$$n=\frac{3}{2}$$$:

$$7 {\color{red}{\int{t^{\frac{3}{2}} d t}}}=7 {\color{red}{\frac{t^{1 + \frac{3}{2}}}{1 + \frac{3}{2}}}}=7 {\color{red}{\left(\frac{2 t^{\frac{5}{2}}}{5}\right)}}$$

Portanto,

$$\int{7 t^{\frac{3}{2}} d t} = \frac{14 t^{\frac{5}{2}}}{5}$$

Adicione a constante de integração:

$$\int{7 t^{\frac{3}{2}} d t} = \frac{14 t^{\frac{5}{2}}}{5}+C$$

$$$\int 7 t^{\frac{3}{2}}\, dt = \frac{14 t^{\frac{5}{2}}}{5} + C$$$A