Hello,
Let's assume t=6x+7
x=(t-7)/6
dt=6dx
\(\int\limits{x(6x+7)^8} \, dx = \int\limits { \dfrac{t-7}{6} t^8} \, \dfrac{dt}{6} \\
= \dfrac{1}{36} \int\limits{ (t^{9}-7t^8) \, dt = \dfrac{1}{36} ( \dfrac{t^{10}}{10}- \dfrac{7t^9}{9} )+C\\
= \dfrac{(6x+7)^9*(54x-7)}{3240} +C\)
