∫ − 2 2 ( 3 u + 1 ) 2 d u = ∫ ( 9 u 2 + 6 u + 1 ) d u = 3 u 3 + 3 u 2 + u | − 2 2 = 3 ⋅ 2 3 + 3 ⋅ 2 2 + 2 − 3 ⋅ − 2 3 + 3 ⋅ − 2 2 − 2 = 52 {\displaystyle {\begin{aligned}\int _{-2}^{2}({3u+1})^{2}du&=\int (9u^{2}+6u+1)du\\[2ex]&={3u^{3}+3u^{2}+u}{\bigg |}_{-2}^{2}\\[2ex]&={3\cdot 2^{3}+3\cdot 2^{2}+2-3\cdot -2^{3}+3\cdot -2^{2}-2}\\[2ex]&={52}\\[2ex]\end{aligned}}}
![{\displaystyle {\begin{aligned}\int _{-2}^{2}({3u+1})^{2}du&=\int (9u^{2}+6u+1)du\\[2ex]&={3u^{3}+3u^{2}+u}{\bigg |}_{-2}^{2}\\[2ex]&={3\cdot 2^{3}+3\cdot 2^{2}+2-3\cdot -2^{3}+3\cdot -2^{2}-2}\\[2ex]&={52}\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/7e3ed7b5417837dfdd54ae913840d5ac5285c880)