Integral of x^2/(x+2)

1. Aug 23, 2011

1. The problem statement, all variables and given/known data

Evaluate the integral:
$\int \frac{x^2}{x + 2} dx$

2. Relevant equations

There aren't any relevant equations...

3. The attempt at a solution

In these type of problems you have to set $u = \text{something}$ so I tried setting $u = x^2$, but then $\text{du} = 2x\text{dx}$ and you can't substitute anything. And if $u = x + 2$ then $\text{du} = 1$ and that's useless.

Also, this problem is from the Swokowski calculus textbook (school starts in two days for me so I'm doing self study )

Last edited: Aug 23, 2011
2. Aug 23, 2011

gb7nash

Before you do anything, do polynomial division (degree of top >= degree of bottom). Once this is done, it should be trivial to take the integral.

3. Aug 23, 2011

1MileCrash

Try doing some algebra first. You can rewrite that. Polynomial long division.

4. Aug 23, 2011

SteamKing

Staff Emeritus
In you second substitution, where u = x+2, du = dx not du = 1

If you carry thru with this substitution properly, you can find the desired integral.

5. Aug 23, 2011

Clearly $\frac{x^2}{x + 2} = x - 2 + \frac{4}{x + 2}$. So integrating that we have $\frac{x^2}{2} - 2x + 4\ln{|x+2|} + C$ where C is a constant.