Homework Help: X((2x^2) - 2)^3 antiderivative

1. Nov 24, 2004

buffgilville

how do I find to antiderivative of:

x((2x^2) - 2)^3

2. Nov 24, 2004

ehild

x(2x^2-2)^3=8x(x^2-1). Replace x^2-1 by t, notice that dt=2dx, so

$$\int x(2x^2-2)^3dx=\int 4 t^3 dt$$

then replace back

$$t=x^2-1$$

ehild

Last edited: Nov 25, 2004
3. Nov 24, 2004

buffgilville

from there I was suppose to compute as x is goes from 0 to 1
I got 0, but the answer is -1

4. Nov 25, 2004

ehild

There was a typo in my message. It is

$$\int x(2x^2-2)^3dx=\int 4 t^3 dt$$

correctly, which is t^4= (x^2-1)^4.

$$\big[(x^2-1)^4\big]_0^1=(1-1)^4-(0-1)^4=-1$$

ehild