∫ ( 3 x − 2 ) 20 d x {\displaystyle \int (3x-2)^{20}dx}
u = 3 x − 2 d u = 3 d x 1 3 d u = d x {\displaystyle {\begin{aligned}u&=3x-2\\[2ex]du&=3dx\\[2ex]{\frac {1}{3}}du&=dx\\[2ex]\end{aligned}}}
∫ u 20 ⋅ 1 3 d u = 1 3 ∫ u 20 d u = 1 3 ⋅ 1 20 + 1 u 20 + 1 = 1 3 ⋅ 1 21 u 21 = 1 63 u 21 + c = 1 63 ( 3 x − 2 ) 21 + c {\displaystyle {\begin{aligned}\int u^{20}\cdot {\frac {1}{3}}du\\[2ex]&={\frac {1}{3}}\int u^{20}du&={\frac {1}{3}}\cdot {\frac {1}{20+1}}u^{20+1}&={\frac {1}{3}}\cdot {\frac {1}{21}}u^{21}&={\frac {1}{63}}u^{21}+c&={\frac {1}{63}}(3x-2)^{21}+c\end{aligned}}}
</math> &= \frac{1}{63} (3x^21-2097152) + c
![{\displaystyle {\begin{aligned}u&=3x-2\\[2ex]du&=3dx\\[2ex]{\frac {1}{3}}du&=dx\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/45bebb73a627f87f28c7b799f9d7ce3e8d4e6fd5)
![{\displaystyle {\begin{aligned}\int u^{20}\cdot {\frac {1}{3}}du\\[2ex]&={\frac {1}{3}}\int u^{20}du&={\frac {1}{3}}\cdot {\frac {1}{20+1}}u^{20+1}&={\frac {1}{3}}\cdot {\frac {1}{21}}u^{21}&={\frac {1}{63}}u^{21}+c&={\frac {1}{63}}(3x-2)^{21}+c\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/504d7bdccf3dc2ef9663dd875868f1329b9c7594)