What is the antiderivative of 5x^4?

To determine the antiderivative of the function (5x^4), we start by applying the power rule for integration. The power rule states that the antiderivative of (x^n) is given by (\frac{x^{n+1}}{n+1} + C), where (C) is the constant of integration.

In the case of (5x^4), we can factor out the constant (5) and focus on integrating (x^4). Using the power rule, we find:

[

\int x^4 , dx = \frac{x^{4+1}}{4+1} + C = \frac{x^5}{5} + C

]

Now, multiplying this result by (5) to account for the original function, we have:

[

\int 5x^4 , dx = 5 \left(\frac{x^5}{5}\right) + C = x^5 + C

]

Thus, the correct antiderivative of (5x^4) is (x^5 + C).

The choice represented by ((5/5)x^5 + C