7.1 Integration By Parts/65

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_{1}^{4}xf''(x)dx\\[2ex] u=x\qquad dv=f''(x)\cdot\;(dx)\qquad \\[2ex] du=dx\qquad v=f'(x)\qquad \\[2ex] \int_{1}^{4}xf''(x)dx&=x\cdot\;f'(x)\bigg|_{1}^{4}-\int_{1}^{4}f'(x)dx \\[2ex] &= x\cdot\;f'(x)-f(x)\bigg|_{1}^{4}\\[2ex] &= (4\cdot\;f'(4)-f(4))-(1\cdot\;f'(1)-f(1))\\[2ex] &= (4\cdot\;3-7)-(5-2) \\[2ex] &= (12-7)-(3)\\[2ex] &=(5)-(3)\\[2ex] &=2 \end{align} }