Help finding indefinite integral?

Question

I need help finding the indefinite integral $$\int \ln \left(\frac{2}{x}\right)$$

I get $x\ln\left(\frac{2}{x}\right)+1$ but my teacher gave us $x\ln 2-x\ln x+x+c$ as the correct answer. I'm not sure on how he got that.

Answer 1

you can use: $\ln\dfrac{a}{b}=\ln a-\ln b$,

$$\int \ln \dfrac{2}{x}\,dx=\int \ln 2 - \ln x\,dx=\int \ln 2 \, dx-\int \ln x \,dx$$