William W. answered • 6d

Math and science made easy - learn from a retired engineer

Use a "u" substitution whenever you see the derivative of the complicated part multiplied by the complicated part. In this case the derivative of x^{3} is 3x^{2} and I see the x^{2} (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 = x^{3} + 9 then du/dx = 3x^{2} or dx = du/(3x^{2})

So the integral turns into:

Simplifying it, we get:

1/3∫u^{7}du = 1/3(1/8)u^{8} = 1/24(x^{3} + 9)^{8} + C (answer 1)