Integral de $$$4096 s^{94}$$$

Encontre $$$\int 4096 s^{94}\, ds$$$.

Aplique a regra do múltiplo constante $$$\int c f{\left(s \right)}\, ds = c \int f{\left(s \right)}\, ds$$$ usando $$$c=4096$$$ e $$$f{\left(s \right)} = s^{94}$$$:

$${\color{red}{\int{4096 s^{94} d s}}} = {\color{red}{\left(4096 \int{s^{94} d s}\right)}}$$

Aplique a regra da potência $$$\int s^{n}\, ds = \frac{s^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ com $$$n=94$$$:

$$4096 {\color{red}{\int{s^{94} d s}}}=4096 {\color{red}{\frac{s^{1 + 94}}{1 + 94}}}=4096 {\color{red}{\left(\frac{s^{95}}{95}\right)}}$$

Portanto,

$$\int{4096 s^{94} d s} = \frac{4096 s^{95}}{95}$$

Adicione a constante de integração:

$$\int{4096 s^{94} d s} = \frac{4096 s^{95}}{95}+C$$

$$$\int 4096 s^{94}\, ds = \frac{4096 s^{95}}{95} + C$$$A