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 }

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

${\begin{aligned}\int {\frac {1}{\sqrt {t}}}\cos {({\sqrt {t}})}dt&=2\int \cos {u}\;du\\[2ex]&=2\sin {u}+c\\[2ex]&=2\sin({\sqrt {t}})+c\\[2ex]\end{aligned}}$