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Some weird integral with natural logarithm

  • Thread starter mrdoe
  • Start date
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1. Homework Statement

[tex]\displaystyle\int\left(\dfrac{\ln x}{x}\right)^2 dx[/tex]

2. The attempt at a solution

I tried letting [tex]u=\ln^2 x[/tex] and dv the rest and I also tried [tex]dv=\ln^2 x dx[/tex] and u the rest. It won't work out.
 
Let u = ln(x), => du = 1/x dx.

Then your integrand is [(u^2) / x]du

Well, x = exp(u), so what you really have is (u^2)exp(-u)du

Does that work? You should be able to handle that one...
 

djeitnstine

Gold Member
614
0
1. Homework Statement

[tex]\displaystyle\int\left(\dfrac{\ln x}{x}\right)^2 dx[/tex]

2. The attempt at a solution

I tried letting [tex]u=\ln^2 x[/tex] and dv the rest and I also tried [tex]dv=\ln^2 x dx[/tex] and u the rest. It won't work out.
your dv is wrong its [tex]dv=\frac{1}{x^2} dx[/tex]
 

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