5.5 The Substitution Rule/2

$\int x^{3}(2+x^{4})^{5}dx{\text{,}}\quad u=2+x^{4}$

${\begin{aligned}u&=2+x^{4}\\[2ex]du&=4x^{3}dx\\[2ex]{\frac {1}{4}}du&=x^{3}dx\end{aligned}}$

$\int x^{3}(2+x^{4})^{5}dx=\int x^{3}dx(2+x^{4})=\int \left({\frac {1}{4}}du\right)(u)={\frac {1}{4}}\int udu$