5.5 The Substitution Rule/53

$\int _{0}^{1}x^{2}(1+2x^{3})^{5}dr$

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

${\begin{aligned}du&=6x^{2}dx\\[2ex]\end{aligned}}$

${\begin{aligned}\int _{1}^{3}u^{5}{\frac {1}{6}}du\\[2ex]\end{aligned}}$

${\begin{aligned}&={\frac {1}{6}}\int _{1}^{3}u^{5}du\\[2ex]\end{aligned}}$

${\begin{aligned}&={\frac {1}{36}}(1+2x^{3})^{6}\end{aligned}}$

${\begin{aligned}&={\frac {181}{9}}\\[2ex]\end{aligned}}$