y = x 2 y = 2 ( x 2 + 1 ) {\displaystyle {\begin{aligned}&\color {red}\mathbf {y=x^{2}} &\color {royalblue}\mathbf {y={\frac {2}{({x^{2}}+1)}}} \\\end{aligned}}}
∫ 1 − 1 ( 2 ( x 2 + 1 ) ) − ( x 2 ) d x = ∫ 1 − 1 ( 2 ⋅ 1 ( x 2 + 1 ) ) − ( x 2 ) d x = [ ( 2 a r c t a n ( x ) − x 3 3 ) ] | − 1 2 {\displaystyle {\begin{aligned}\int _{1}^{-1}\left({\frac {2}{({x^{2}}+1)}}\right)-\left(x^{2}\right)dx=\int _{1}^{-1}\left(2\cdot {\frac {1}{(x^{2}+1)}}\right)-\left(x^{2}\right)dx&=\left[(2arctan(x)-{\frac {x^{3}}{3}})\right]{\Bigg |}_{-1}^{2}\\[2ex]\end{aligned}}}
![{\displaystyle {\begin{aligned}\int _{1}^{-1}\left({\frac {2}{({x^{2}}+1)}}\right)-\left(x^{2}\right)dx=\int _{1}^{-1}\left(2\cdot {\frac {1}{(x^{2}+1)}}\right)-\left(x^{2}\right)dx&=\left[(2arctan(x)-{\frac {x^{3}}{3}})\right]{\Bigg |}_{-1}^{2}\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/f13acae77c36ef194b62134a8659078cbb32df7a)
