∫ 0 2 ( x − 1 ) 25 d x = ∫ t 25 d t = t 25 26 = ( x − 1 ) 26 26 | 0 2 = ( 2 − 1 ) 26 26 − ( 0 − 1 ) 26 26 = 0 {\displaystyle {\begin{aligned}&\int _{0}^{2}({x-1})^{25}dx\\[2ex]&=\int {t^{25}}dt\\[2ex]&={\cfrac {t^{25}}{26}}\\[2ex]&={\cfrac {(x-1)^{26}}{26}}{\bigg |}_{0}^{2}\\[2ex]&={\cfrac {(2-1)^{26}}{26}}-{\cfrac {(0-1)^{26}}{26}}\\[2ex]&=0\end{aligned}}}
![{\displaystyle {\begin{aligned}&\int _{0}^{2}({x-1})^{25}dx\\[2ex]&=\int {t^{25}}dt\\[2ex]&={\cfrac {t^{25}}{26}}\\[2ex]&={\cfrac {(x-1)^{26}}{26}}{\bigg |}_{0}^{2}\\[2ex]&={\cfrac {(2-1)^{26}}{26}}-{\cfrac {(0-1)^{26}}{26}}\\[2ex]&=0\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/c50ac96b54d5e824e15669fc5aea9fe486e6025f)