5.5 The Substitution Rule/15

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 sin(\pi t) dt \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} let \; u &=\pi t \\[2ex] du &= \pi dx \\[2ex] \frac{1}{\pi}du &= dx \end{align} }

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