# Some weird integral with natural logarithm

#### mrdoe

1. 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.

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#### csprof2000

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
1. 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.
your dv is wrong its $$dv=\frac{1}{x^2} dx$$

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