∫ 0 π ( t s i n 3 t ) d t = ∫ 0 π 1 2 t 2 1 2 s i n 3 t 2 = ∫ 0 π 1 2 π 2 1 2 s i n 3 π 2 {\displaystyle \int _{0}^{\pi }(tsin3t)dt{\begin{aligned}&=\int _{0}^{\pi }{\frac {1}{2}}t^{2}{\frac {1}{2}}sin3t^{2}\\[2ex]&=\int _{0}^{\pi }{\frac {1}{2}}\pi ^{2}{\frac {1}{2}}sin3\pi ^{2}\\[2ex]\end{aligned}}}
![{\displaystyle \int _{0}^{\pi }(tsin3t)dt{\begin{aligned}&=\int _{0}^{\pi }{\frac {1}{2}}t^{2}{\frac {1}{2}}sin3t^{2}\\[2ex]&=\int _{0}^{\pi }{\frac {1}{2}}\pi ^{2}{\frac {1}{2}}sin3\pi ^{2}\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/8a0d239d918edd96377ac0ab526e3e7d9248e90a)