7.1 Integration By Parts/51b

${\text{Use exercise 47 to evaluate}}\int (\ln {x})^{3}dx$

${\text{Exercise 47: }}x(\ln {x})^{n}-n\int (\ln {x})^{n-1}dx$

Failed to parse (unknown function "\quadd"): {\displaystyle \begin{align} \int\ln(x)^3dx &= x\ln(x)^3 -3\underbrace{\int\ln(x)^2dx}_{ \begin{aligned} u &= \ln^{2}{x} \quadd dv=dx \\[2ex] du &= \frac{2}{x}\ln{(x)}dx \quad v=x \\[2ex] \end{aligned} } \end{align} }