Math Help - Easy u-substitution

1. Easy u-substitution

integrate 2 / x+3

2. If it's so easy, why didn't you do it? :O

Sub $u = x+3$

3. why didn't I do it?

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.

4. Originally Posted by Retromingent
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 $2 \ln | x+3 |$.

Before starting the integral, you should factor out the constants so $\int \frac{2}{x+3} = 2\int \frac{1}{x+3}$.

If you are unsure about your answer, differentiate it, $\frac{\mathrm{d}(2 \ln | x+3|)}{\mathrm{d}x}$, to see if you get the initial integration variable.