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 (unknown function "\begin{align}"): {\displaystyle \begin{align} \int_{1}^{2}\frac{\ln{x}^2}{x^3} & = -\frac{\ln^2{(x)}}{2x^2} - \int-\frac{\ln{(x)}{x^3} \\[2ex] & = -\frac{\ln{(x)}}{2x^2} - \frac{1}{2}\int\frac{1}{x^3} \\[2ex] & = -\frac{\ln{(x)}}{2x^2} - \frac{1}{4x^2} \end{align} }