Use a "u" substitution whenever you see the derivative of the complicated part multiplied by the complicated part. In this case the derivative of x3 is 3x2 and I see the x2 (the 3 isn't important) outside the complicated part being multiplied by it. That's a dead giveaway of the use of the chain rule.
So let u = x3 + 9 then du/dx = 3x2 or dx = du/(3x2)
So the integral turns into:
Simplifying it, we get:
1/3∫u7du = 1/3(1/8)u8 = 1/24(x3 + 9)8 + C (answer 1)