7.1 Integration By Parts/28

$\int _{1}^{2}{\frac {(\ln {x}^{2})}{x^{3}}}$

$u=\ln {x}\qquad dv={\frac {1}{x^{3}}}$

$du={\frac {1}{x}}\qquad v=-{\frac {1}{2x^{2}}}$

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}^{2}\frac{\ln{x}^2}{x^3} & = -\frac{\ln{(x)}}{2x^2} - \int-\frac{1}{2x^3} \\[2ex] & = -\frac{\ln{(x)}}{2x^2} - \frac{1}{2}\int\frac{1}{x^3} \\[2ex] & = \end{align} }