∫ 1 2 y + 5 y 7 y 3 d y = ∫ 1 2 ( y y 3 + 5 y 7 y 3 ) d y = ∫ 1 2 ( y − 2 + 5 y 4 ) d y = y − 2 + 1 − 2 + 1 + 5 y 4 + 1 4 + 1 | 1 2 {\displaystyle {\begin{aligned}\int _{1}^{2}{\frac {y+5y^{7}}{y^{3}}}dy&=\int _{1}^{2}\left({\frac {y}{y^{3}}}+{\frac {5y^{7}}{y^{3}}}\right)dy=\int _{1}^{2}(y^{-2}+5y^{4})dy\\[2ex]&={\frac {y^{-2+1}}{-2+1}}+{\frac {5y^{4+1}}{4+1}}{\bigg |}_{1}^{2}\end{aligned}}}
![{\displaystyle {\begin{aligned}\int _{1}^{2}{\frac {y+5y^{7}}{y^{3}}}dy&=\int _{1}^{2}\left({\frac {y}{y^{3}}}+{\frac {5y^{7}}{y^{3}}}\right)dy=\int _{1}^{2}(y^{-2}+5y^{4})dy\\[2ex]&={\frac {y^{-2+1}}{-2+1}}+{\frac {5y^{4+1}}{4+1}}{\bigg |}_{1}^{2}\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/20a89c255c1a0244952d403ff5d023c8a8039a5a)