$$\int\_3^9 \frac{1}{x \log x} \,\mathrm dx$$

I tried : 

$$u=\log x \implies x \ln 10 du = dx$$

$$\ln 10 \int\_{\log 3}^{2\log 3} \frac{1}{u} du = \ln 10 \left[\ln u \right]\_{\log 3}^{2\log 3}=\ln 10 \left[\ln(2 \ln 3)-\ln(\ln 3) \right]=$$

$$\ln 10 \left[\ln\frac{2 \ln 3}{(\ln 3)} \right]=\ln 10 \cdot \ln 2$$

But this isn't correct, why?