Z(x^5− x^2)(x^6− 2x^3)^2011dx

Thank you so much!

I guess Z means integral

Let u = x^6 - 2x^3
du = 6x^5 - 6x = 6(x^5 - x^2)

My, my. How convenient.
So, you have

Z(u^2011 * du/6)
= 1/6 Z(u^2011) du
= 1/6 * 1/2012 * u^2012
= 1/12072 (x^6 - 2x^3)^2012