5.5 The Substitution Rule/21

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 \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 (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} \int \frac{\cos{(\sqrt{t})}}{\sqrt{t}} dt &= 2\int \cos {u}\;du \\[2ex] &= 2 \sin{u}+c \\[2ex] &= 2 \sin(\sqrt{t}) + c \\[2ex] \end{align} }