The thing to remember for these types of questions is that the region you require is
by the chain rule.
so for you we have
Now you need to find your values of a and b, well they are when x = ln(4) and x = ln(2), look at your expression for x and you see that these occur when t = 2 and 0 respectively.
So putting it all together we have
as required, which you can solve using partial fractions