∫ s i n ( π t ) d t {\displaystyle {\begin{aligned}\ \int sin(\pi t)dt\end{aligned}}}
u = π t d u = π d x 1 π d u = d x {\displaystyle {\begin{aligned}u&=\pi t\\[2ex]du&=\pi dx\\[2ex]{\frac {1}{\pi }}du&=dx\end{aligned}}}
∫ s i n ( π t ) d t = ∫ s i n ( u ) ( 1 π d u ) = ∫ 1 π ( − c o s ( u ) ) + C = ∫ − 1 π c o s π t + C {\displaystyle {\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}}}
![{\displaystyle {\begin{aligned}u&=\pi t\\[2ex]du&=\pi dx\\[2ex]{\frac {1}{\pi }}du&=dx\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/126a42420590e5b1005c3db1fa48ce27ccf36306)
