The integral \(\int\left(\dfrac{\ln x}{x}\right)^2 dx\) requires a substitution method for evaluation. The correct substitution involves letting \(u = \ln x\), which simplifies the integrand to \((u^2) \cdot e^{-u} du\). An incorrect approach was noted where \(dv\) was initially set as \(\ln^2 x dx\), which does not yield a solvable form. The proper differential \(dv\) should be \(\frac{1}{x^2} dx\) for accurate integration.
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mrdoe said:Homework Statement
\displaystyle\int\left(\dfrac{\ln x}{x}\right)^2 dx
2. The attempt at a solution
I tried letting u=\ln^2 x and dv the rest and I also tried dv=\ln^2 x dx and u the rest. It won't work out.