5.5 The Substitution Rule/55

$\int _{0}^{\pi }\sec ^{2}\left({\frac {t}{4}}\right)dt$

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 &= \frac{t}{4} \\[2ex] du &= \frac{1}{4}dt \\[2ex] 4du &=dx \end{align} }

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_{0}^{\pi} \sec^2\left(\frac{t}{4}\right)dt &= 4\int_{0}^{\pi} \sec^2(u)du \\[2ex] &= 4\cdot \tan^2(u) = 4\cdot \tan^2\left(\frac{1}{4}\right)\bigg|_{0}^{\pi} \\[2ex] \end{align} }