integrate 2 / x+3
LOL! I think the answer is 2ln|x+3|. It's the constant multiple rule that throws me (which I believe is how that 2 is pulled out). It's easy to operate, but I don't understand it. That is, I do not understand why that 2 can be omitted from integration.
Yes, you are correct, it is $\displaystyle 2 \ln | x+3 |$.
Before starting the integral, you should factor out the constants so $\displaystyle \int \frac{2}{x+3} = 2\int \frac{1}{x+3}$.
If you are unsure about your answer, differentiate it, $\displaystyle \frac{\mathrm{d}(2 \ln | x+3|)}{\mathrm{d}x}$, to see if you get the initial integration variable.