Answer
$$\frac{1}{{2{a^2}\left( {{a^2} - {x^2}} \right)}} - \frac{1}{{2{a^4}}}\ln \left( {{x^2} - {a^2}} \right) + 2\ln \left( x \right) + C$$
Work Step by Step
$$\eqalign{
& {\text{Integrate using a computer algebra system as the book says}} \cr
& {\text{Using wolfram alpha we obtain:}} \cr} $$