Explanation

(a)
$\int_{}^{}{\frac{x^{2}}{x^{2} + 4}\ dx} = \int_{}^{}{\frac{x^{2} + 4 - 4}{(x^{2} + 4)}dx}$
$= \int_{}^{}{\left( \frac{x^{2} + 4}{x^{2} + 4} - \frac{4}{x^{2} + 4} \right)dx}$
$= \int_{}^{}{\left\lbrack 1 - \frac{4}{x^{2} + 4} \right\rbrack dx = \int_{}^{}{dx - \int_{}^{}{\frac{4}{x^{2} + 4}dx}}}$
$= x - 4\int_{}^{}{\frac{dx}{x^{2} + (2)^{2}} = x - \frac{4}{2}\tan^{- 1}{\frac{x}{2} + c}}$
$= x - 2\tan^{- 1}{\frac{x}{2} + c}$