Evaluate the integral.
\[
\int 9 y^{4} \sqrt{1-9 y^{5}} d y
\]

Step 1 ：Let's start by identifying a part of the integrand that could be a good choice for a u-substitution. The function inside the square root, \(1-9y^5\), seems like a good choice because its derivative, \(-45y^4\), is similar to the other part of the integrand, \(9y^4\).

Step 2 ：Let's make the substitution \(u = 1 - 9y^5\). The derivative of \(u\) with respect to \(y\) is \(du/dy = -45y^4\).

Step 3 ：Substituting \(u\) into the integral, we get \(-\frac{1}{5}\sqrt{u}\).

Step 4 ：Now, we can easily integrate this function with respect to \(u\). The integral of \(-\frac{1}{5}\sqrt{u}\) is \(-\frac{2}{15}u^{3/2}\).

Step 5 ：Finally, we substitute \(u\) back in terms of \(y\) to get the final answer. The final integral is \(-\frac{2}{15}(1 - 9y^5)^{3/2}\).

Step 6 ：So, the integral of \(9y^4\sqrt{1-9y^5}\) with respect to \(y\) is \(\boxed{-\frac{2}{15}(1 - 9y^5)^{3/2}}\).