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Integration by Substitution

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Question

Evaluate $\int (log x)^{2} d x$ .

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Solution

$\begin{matrix} \int {(log x)}^{2} 4 = {(log x)}^{2} d u = \frac{2; o g x}{x} d x [\begin{matrix} V = x D V = d x \end{matrix}] \int {(log x)}^{2} d x = \int u d v = u v - \int u d v = x {(log x)}^{2} - 2 (x log x - x) + c = x {(log x)}^{2} 2 x log x + 2 x + c \end{matrix}$

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