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 arctan ( x ) − x 3 3 ] | − 1 1 = [ 2 arctan ( 1 ) − ( 1 ) 3 3 ] − [ ( 2 arctan ( − 1 ) − ( − 1 ) 3 3 ] {\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\\[2ex]=\left[2\arctan(x)-{\frac {x^{3}}{3}}\right]{\Bigg |}_{-1}^{1}\\[2ex]=\left[2\arctan(1)-{\frac {(1)^{3}}{3}}\right]-\left[(2\arctan(-1)-{\frac {(-1)^{3}}{3}}\right]\\[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\\[2ex]=\left[2\arctan(x)-{\frac {x^{3}}{3}}\right]{\Bigg |}_{-1}^{1}\\[2ex]=\left[2\arctan(1)-{\frac {(1)^{3}}{3}}\right]-\left[(2\arctan(-1)-{\frac {(-1)^{3}}{3}}\right]\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/1f0e655c975d54be5ad7ea20fc30a2bf6aef2d73)
