Question

determine the general anti - derivative for the following function. use an uppercase ( c ) as your arbitrary constant.( h(x)=e^{x}+x^{5} )( h(x)=)

Explanation:

Step1: Anti-derive $e^x$

The anti-derivative of $e^x$ is $e^x$.

Step2: Anti-derive $x^5$

Use power rule: $\int x^n dx = \frac{x^{n+1}}{n+1}$. For $n=5$, $\int x^5 dx = \frac{x^{6}}{6}$.

Step3: Add arbitrary constant

Combine results and add uppercase $C$.

Answer:

$e^x + \frac{x^6}{6} + C$