5.5 The Substitution Rule/21

$\int {\frac {\cos {({\sqrt {t}})}}{\sqrt {t}}}dt=2\int \cos {u}du=2\sin {u}+c=2\sin({\sqrt {u}})+c$

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

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} 2\int \cos {u} du &= 2 \sin{u}+c \\[2ex] &= 2 \sin(\sqrt{u}) + c \\[2ex] \end{align} }