Is the answer to integrate x/x+3dx this:

ln|x+3|+c ????

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- Apr 22nd 2008, 08:54 AMnavynukejonesBasic integral problem.
Is the answer to integrate x/x+3dx this:

ln|x+3|+c ???? - Apr 22nd 2008, 09:01 AMIsomorphism
- Apr 22nd 2008, 09:40 AMnavynukejonesAre you sure?
I think you have to use the formula: the integral of du/u = ln|u|+C and in this problem u=x+3 and therefore du=dx.

- Apr 22nd 2008, 09:44 AMdisclaimer
- Apr 22nd 2008, 09:51 AMIsomorphism

Just observe carefully.... there is a x term in the numerator. So according to you u = x+3, du = dx.

So $\displaystyle \int \frac{x}{x+3} \, dx = \int \frac{x}{u} \, du$

But hey you have to get rid of that x in the above expression(Wait)

Thats why write $\displaystyle \frac{x}{x+3} = 1 - \frac{3}{x+3}$. Both the terms now are easily integrable :D - Apr 22nd 2008, 02:12 PMMathstud28