5.5 The Substitution Rule/55

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int _{0}^{\pi }\sec ^{2}\left({\frac {t}{4}}\right)dt}

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}u&={\frac {t}{4}}\\[2ex]du&={\frac {1}{4}}dt\\[2ex]4du&=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} \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{t}{4}\right)\bigg|_{0}^{\pi} \\[2ex] &= 4\cdot \tan^2\left(\frac{\pi}{4}\right)-4\cdot \tan^2\left(\frac{0}{4}\right) \\[2ex] &= 4-0 \\[2ex] &= 4 \end{align} }