# Some weird integral with natural logarithm

1. Mar 2, 2009

### mrdoe

1. The problem statement, all variables and given/known data

$$\displaystyle\int\left(\dfrac{\ln x}{x}\right)^2 dx$$

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.

2. Mar 2, 2009

### 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...

3. Mar 2, 2009

### djeitnstine

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