$$ \int_8^{18} \frac{1}{(x+2) \sqrt{x-3}} d x= $$

If [.] denotes the greatest integer function, then $\int_1^2\left[x^2\right] d x=$

$$ \mathop {\lim }\limits_{n \to \infty } \frac{1}{n^2}\left[e^{1 / n}+2 e^{2 / n}+3 e^{3 / n}+\ldots+2 n e^2\right]= $$

Let $m, n, p, q$ be four positive integers. If

$$ \begin{aligned} & \int_0^{2 \pi} \sin ^m x \cos ^n x d x=4 \int_0^{\pi / 2} \sin ^m x \cos ^n x d x \int_0^{2 \pi} \sin ^p x \cos ^n x d x=0 \\ & \int_0^\pi \sin ^p x \cos ^q x d x=0, a=m+n+p \text { and } b=m+n+q, \text { then } \end{aligned} $$