7.1 Integration By Parts/19

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}\int _{0}^{\pi }(tsin3t)dt\\[2ex]&=\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]&={\frac {\pi }{3}}\end{aligned}}}