Evaluate the integral.
$$\int 9y^4\sqrt{1-9y^5}dy$$

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 $\boxed{{\displaystyle -\frac{2}{15}(1-9y^5{)}^{3/2}}}$.