Thread: Calc integration using substitution

Integrate: (x^2)((x^3)-1)^4)dx
I got:
U=(x^3)-1 then dU=((x^3)-1)dx then dU/((x^3)-1) so finally I have: Integrate ((x^2)(U^4)dU)/((x^3)-1).
Now what?

Your u should be x^3-1. You derivate u, and get 3x^2dx. Your dx then becomes 1/3x^2du. Substitute into your equation and you get 1/3u^4. Integrate. You get 1/15u^5. Substitute your x^3-1 back in to get 1/5(x^3-1)^5+C.