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

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

Apply the constant multiple rule $$$\int c f{\left(s \right)}\, ds = c \int f{\left(s \right)}\, ds$$$ with $$$c=4096$$$ and $$$f{\left(s \right)} = s^{94}$$$:

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

Apply the power rule $$$\int s^{n}\, ds = \frac{s^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=94$$$:

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

Therefore,

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

Add the constant of integration:

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

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