5.5 The Substitution Rule/21

$\int {\frac {\cos {({\sqrt {t}})}}{\sqrt {t}}}dt=2\int cosudu={\frac {2}{3}}u^{2/3}+c=$

${\begin{aligned}u&={\sqrt {u}}\\[2ex]du&={\frac {1}{2}}\ {\frac {1}{\sqrt {t}}}dx\\[2ex]2du&={\frac {1}{\sqrt {t}}}dx\end{aligned}}$