Determine the following indefinite integral. Check your work by differentiation. \[ \int \sqrt[5]{r^{4}} d r \]

Step 1 ：We are given the integral \(\int \sqrt[5]{r^{4}} dr\), which is of the form \(\int x^n dx\), where \(n\) is a real number.

Step 2 ：We can apply the power rule for integration, which states that \(\int x^n dx = \frac{1}{n+1}x^{n+1} + C\), where \(C\) is the constant of integration.

Step 3 ：In this case, \(n = \frac{4}{5}\), so applying the power rule gives us \(\frac{5}{9}r^{1.8} + C\).

Step 4 ：To check our work, we can differentiate this result. The derivative of \(\frac{5}{9}r^{1.8}\) is \(r^{0.8}\), which matches the original function.

Step 5 ：Thus, the indefinite integral of \(\sqrt[5]{r^{4}}\) with respect to \(r\) is \(\boxed{\frac{5}{9}r^{1.8} + C}\), where \(C\) is the constant of integration.