Let the domain of the function f(x)= log_2 log_4 log_6(3+4 x-x^2) be (a, b). If ∫_0^b-a[x^2] d x=p-√ q -√ r, p, q, r ∈ N, gcd (p, q, r)=1, where [·]…

Let the domain of the function $\displaystyle f(x)=\log _2 \log _4 \log _6\left(3+4 x-x^2\right)$ be $\displaystyle (a, b)$. If $\displaystyle \int_0^{b-a}\left[x^2\right] d x=p-\sqrt{q}-\sqrt{r}, p, q, r \in \mathbb{N}, \operatorname{gcd}(p, q, r)=1$, where $\displaystyle [\cdot]$ is the greatest integer function, then $\displaystyle p+q+r$ is equal to