Let the slope of the line \( 45x + 5y + 3 = 0 \) be \( 27r_1 + \dfrac{9r_2}{2} \) for some \( r_1, r_2 \in \mathbb{R} \).
Then \(\displaystyle\lim_{x \to 3} \left( \int_{3}^{x} \dfrac{8t^2}{\dfrac{3r_2 x}{2} - r_2 x^2 - r_1 x^3 - 3x} dt \right)\) is equal to __________.
