I'm not sure how to finish this problem:

Evaluate the definate integral from 0 to 1 x^2(1 + 2x^3)^5 dx

1. u = 1 + 2x^3

2. du/dx = 6x^2

3. du = 6x^2 dx , du/6 = x^2 dx

x = 0, u = 1 + 2(0)^3 = 1

x = 1, u = 1 + 2(1)^3 = 3

I'm not sure what to do next. What I'm doing is not working. The answer is supposed to be 182/9.