7.1 Integration By Parts/7

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 x^2 sin (\pi x)\\[2ex] U=x^2 ,\\[2ex] du= 2xdx ,\\[2ex] dv= sin(\pi x)dx ,\\[2ex] v=-\frac{1}{\pi}cos(\pi x) \\[2ex] &=-\frac{x^2}{\pi}cos(\pi x) +\frac{2}{\pi} \int x cos (\pi x) dx\\[2ex] U=x,\\[2ex] du= dx,\\[2ex] dv= cos(\pi x) dx,\\[2ex] v=\frac{1}{\pi}sin (\pi x) \\[2ex] &=-\frac{x^2}{\pi}cos(\pi x)+ \frac{2}{\pi}[\frac{x}{\pi}sin(\pi x) - \frac{1}{\pi}\int sin (\pi x) dx]\\[2ex] &= -\frac{x^2}{\pi}cos(\pi x)+ \frac{2}{\pi}[\frac{x}{\pi}sin(\pi x) - \frac{1}{\pi^2}cos(\pi x) ] +c\\[2ex] \end{align} }