∫ x 3 ( 2 + x 4 ) 5 d x , u = 2 + x 4 {\displaystyle \int x^{3}(2+x^{4})^{5}dx{\text{,}}\quad u=2+x^{4}}
u = 2 + x 4 d u = 4 x 3 d x 1 4 d u = x 3 d x {\displaystyle {\begin{aligned}u&=2+x^{4}\\[2ex]du&=4x^{3}dx\\[2ex]{\frac {1}{4}}du&=x^{3}dx\end{aligned}}}
∫ x 3 ( 2 + x 4 ) 5 d x = ∫ x 3 d x ( 2 + x 4 ) = ∫ ( 1 4 d u ) ( u ) {\displaystyle \int x^{3}(2+x^{4})^{5}dx=\int x^{3}dx(2+x^{4})=\int \left({\frac {1}{4}}du\right)(u)}
![{\displaystyle {\begin{aligned}u&=2+x^{4}\\[2ex]du&=4x^{3}dx\\[2ex]{\frac {1}{4}}du&=x^{3}dx\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/f335b2b6157a7fb6b55606e357e96925c77fcfb8)
