# 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.