The form of the expression in the denominator clearly hints that a reduction is possible by rationalization which would lead to a constant term in the denominator:
The first simplification by rationalization led to an expression which involved two terms of the form ; to integrate these terms, we wrote the outside the root as so that a final expression is obtained which contains only terms of the form ; these could then be integrated easily.
We simply both the numerator and the denominator separately :
Notice that , so that
The required integral is now easy to evaluate :
Taking cue from Example-, our aim should be to somehow get rid of the variable term in the denominator; to do this, we write the numerator as :