7.1 Integration By Parts/35

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_\sqrt{\frac{{\pi}}{2}}^\sqrt{\pi}\ \theta^3 cos(\theta^2) d\theta & u=\theta^2 \\[2ex] & du= 2\theta d\theta \\[2ex] & \frac{1}{2}du=\theta d\theta \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} & \int{}^{} u\cdot cos(u) du & w=u \\[2ex] & wu=du & dv= cos(u) dx & v= sin(u) \end{align} }

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}&u\cdot sin(u)-\int {}^{}sin(u)du&={\frac {1}{2}}u\cdot sin(u)+{\frac {1}{2}}cos(u){\bigg |}_{\frac {\pi }{2}}^{\pi }&={\frac {1}{2}}(\pi )\cdot sin(\pi )+{\frac {1}{2}}cos(\pi )-({\frac {1}{2}}({\frac {\pi }{2}})\cdot sin({\frac {\pi }{2}})+{\frac {1}{2}}cos({\frac {\pi }{2}}))\\[2ex]&={\frac {1}{2}}(\pi )(0)+{\frac {1}{2}}(-1)-({\frac {\pi }{4}}+{\frac {1}{2}}(0)\\[2ex]&=-{\frac {1}{2}}-{\frac {\pi }{4}}\end{aligned}}}