5.5 The Substitution Rule/55

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

${\begin{aligned}u&={\frac {t}{4}}du&={\frac {1}{4}}dt4du&=dx\end{aligned}}$

Failed to parse (unknown function "\begin{align}"): {\displaystyle \begin{align} \int_{0}^(\pi} \sec^2\left(\frac{t}{4}\right)dt &= 4\int_{0}^{\pi} \sec^2(u)du \\[2ex] \end{align} }

= 4\cdot \tan^2(u)