5.5 The Substitution Rule/15

${\begin{aligned}\ \int sin(\pi t)dt\end{aligned}}$

Failed to parse (unknown function "\space"): {\displaystyle \begin{align} let \space u &=\pi t \\[2ex] du &= \pi dx \\[2ex] \frac{1}{\pi}du &= dx \end{align} }

${\begin{aligned}\ \int sin(\pi t)dt=\int sin(u)({\frac {1}{\pi }}du)=\int {\frac {1}{\pi }}(-cos(u))+C=\int -{\frac {1}{\pi }}cos\pi t+C\end{aligned}}$