Question

The integral of x(6x+7)^8

Answer 1

Hello,

Let's assume t=6x+7
x=(t-7)/6
dt=6dx


`\int\limits{x(6x+7)^8} \, dx = \int\limits { (t-7)/(6) t^8} \, (dt)/(6) \\ = (1)/(36) \int\limits{ (t^(9)-7t^8) \, dt = (1)/(36) ( (t^(10))/(10)- (7t^9)/(9) )+C\\ = ((6x+7)^9*(54x-7))/(3240) +C`