Put u = 1 - 2x⁴

Then du = -8x³dx

The question has x³dx so we write

So we have:

NOTE: If we take the second approach, i.e. leaving the variable changed, we have:

u = 1 - 2x⁴.

As x = -1 → 0,

then u = -1 → 1

So the problem becomes:

This second approach is quite useful later when the substitutions become more involved (e.g. trigonometric substitution).