Integration, please help!

Question

Evaluate the integral  

Options:

1. 
2. 
3. 
4. 

Answer 1

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)