Answer
$\dfrac{5^s}{\ln 5} +\dfrac{s^{6}}{6}+C$
Work Step by Step
Calculate the anti-derivative.
Since, we know $\int x^{n} dx=\dfrac{x^{n+1}}{n+1}+c$ and $ \int a^x dx=\dfrac{1}{\ln a} a^x+c$
where $c$ is a constant of proportionality.
Then $\int (5^s+s^5) ds=\int 5^s ds+\int s^5 ds$
or, $= \dfrac{1}{\ln 5} 5^s+\dfrac{s^{5+1}}{5+1}+C$
Thus, $= \dfrac{5^s}{\ln 5} +\dfrac{s^{6}}{6}+C$
