5.5 The Substitution Rule/21

$\int {\frac {\cos {({\sqrt {t}})}}{\sqrt {t}}}\;dt$

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

Failed to parse (unknown function "\begin{align}"): {\displaystyle \begin{align} \int \frac{1}}{\sqrt{t}}\cos{(\sqrt{t}) dt &= 2\int \cos {u}\;du \\[2ex] &= 2 \sin{u}+c \\[2ex] &= 2 \sin(\sqrt{t}) + c \\[2ex] \end{align} }