Thank you much, this is the part I was missing.
Aside:
Let
Derive this equation
Solve for
Manipulate the first equation to make it appear like so that when you substitute dx, the x is eliminated.
Therefore:
Substitute into first equation
Integrate, sub in u and simplfy.
This is a perfect place to use my favourite rule of integration:
So let
You'll notice that it isn't quite a match to what you are trying to integrate. However, if you divide by , it is exactly what you are trying to integrate. Therefore, we can apply the rule as normal, but we must remember to divide our final answer by -2.
I think in this case, this method is much nicer than substitution - if you spot the rule, it will take a few lines of working to obtain the full solution with no messy work required at all.