${\displaystyle \int \frac{8x+13}{\sqrt{4x+7}}dx}$ $=A{(4x+7)}^p+B{(4x+7)}^q+c$ , then $\frac{p+q}{A+B}$  is equal to :

$I={\displaystyle \int \frac{8x+13}{\sqrt{4x+7}}dx}={\displaystyle \int \frac{2(4x+7)-1}{\sqrt{4x+7}}dx}$

   $={\displaystyle \int 2\sqrt{4x+7}dx-{\displaystyle \int {(4x+7)}^{-1/2}dx}}$

   $=\frac{2\times 2}{4\times 3}{(4x+7)}^{3/2}–\frac{2}{4}{(4x+7)}^{1/2}+c$

   $=\frac{1}{3}{(4x+7)}^{3/2}–\frac{1}{2}{(4x+7)}^{1/2}+c$

$\therefore A=1/3,B=–1/2,p=3/2,q=1/2$

$\therefore \frac{p+q}{A+B}=\frac{2}{(-1/6)}=–12$ .