How Do I Find the Antiderivative of x((2x^2) - 2)^3?

[buffgilville]

how do I find to antiderivative of:

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

 

[ehild]

how do I find to antiderivative of:

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

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

 

[buffgilville]

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

 

[ehild]

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

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