두 정적분 합치기

$\displaystyle \int _{2} ^{6} {\frac{x ^{2} ( x ^{2} + 2 x + 4 )}{x + 2}} d x + \int _{6} ^{2} {\frac{4 ( y ^{2} + 2 y + 4 )}{y + 2}} d y$ $\displaystyle = \int _{2} ^{6} {\frac{x ^{2} ( x ^{2} + 2 x + 4 )}{x + 2}} d x - \int _{2} ^{6} {\frac{4 ( x ^{2} + 2 x + 4 )}{x + 2}} d x$ $\displaystyle = \int _{2} ^{6} {\left\{ \frac{x ^{2} ( x ^{2} + 2 x + 4 )}{x + 2} - \frac{4 ( x ^{2} + 2 x + 4 )}{x + 2} \right\}} d x$ $\displaystyle = \int _{2} ^{6} {\frac{\left( x ^{2} - 4 \right) ( x ^{2} + 2 x + 4 )}{x + 2}} d x$ $\displaystyle \begin{aligned} = \int _{2} ^{6} {\left( x - 2 \right) ( x ^{2} + 2 x + 4 )} d x \\ \end{aligned}$ $\displaystyle = \int _{2} ^{6} {\left( x ^{3} - 8 \right)} d x$ $\displaystyle = \left[ \frac{1}{4} x ^{4} - 8 x \right] _{2} ^{6} = 288$