Chapter 4 - Practice Exercises - Page 279: 116

$\dfrac{5^s}{\ln 5} +\dfrac{s^{6}}{6}+C$

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, $= \dfrac{5^s}{\ln 5} +\dfrac{s^{6}}{6}+C$

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