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int (In x)^2/x  dx

 Nov 28, 2016
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int (In x)^2/x  dx

 

\(\int\;\frac{(lnx)^2}{x}\;dx\\ \qquad Let\;\;u=lnx\\ \qquad \frac{du}{dx}=\frac{1}{x}\\ =\int\;u^2\frac{du}{dx}\;dx\\ =\int\;u^2\;du\\ =\frac{u^3}{3}+c\\ =\frac{(lnx)^3}{3}+c\\ \)

 Nov 28, 2016

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