What happens if we try the substitution
y = x2 − 4?
The transformation formula for differentials is
dy = 2x⋅dx and the
expression on the right is not in the integral, which does not sound too
optimistic. When we try to rearrange the differential transformation
formula, we get this.
![](gifc3/pc4dc3ba.gif)
Our suspision is vindicated, the new integral is not any better than the
given one.
Now we will try out our favorite mixed substitution for removing roots, that
is,
y2 = x2 − 4.
Differentials get transformed using the formula
2y⋅dy = 2x⋅dx
and again we have to tweak it a bit.
![](gifc3/pc4dc3bb.gif)
Again, this was not any help.