Integral of x^2/(x+2) Solution | Evaluate the Integral

[professordad]

Homework Statement

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

Homework Equations

There aren't any relevant equations...

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 )

 

[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.

 

[1MileCrash]

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

 

[SteamKing]

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.

 

[professordad]

Wow, I can't believe I missed that. Here's what I have from there:

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.

Thanks for your help guys! I appreciated it

Also, to SteamKing, yes, I made a mistake while typing it up.