Hey zachb.

You have the idea right, I'm just really confused on the last two lines!

u = 1+2x^3

(1/6)du = x^2

Now plug these into your original equation so we can find the answer to the integral and then plug in the limits.

x^2(1+2x^3)dx => (1/6)udu

You can integrate that easily!

(1/12)u^2+C, but since in the end it's a definite integral, forget the C.

So now back substitute.

(1/12)u^2 => (1/12)(1+2x^3)^2.

Now evaluate the limits.

Jameson