Solving Weird Integral Problem: \int (x+8)/(x+4) | AP Calculus Bonus Question

[Totalderiv]

Homework Statement

$$\int (x+8)/(x+4)$$

Homework Equations

N/a

The Attempt at a Solution

I tried to split the problem which resulted in:

$$\int x/(x+4) + \int 8/(x+4)$$

But now I'm stuck,and this is a bonus question on my AP Calculus homework.

 

[gb7nash]

$$\int (x+8)/(x+4)$$

Do polynomial division and it becomes much simpler.

 

[Char. Limit]

It might help to factor it like this:

$$\frac{x+8}{x+4} = \frac{(x+4)+4}{x+4}$$

Then use the same trick you did.

 

[gb7nash]

It might help to factor it like this:

$$\frac{x+8}{x+4} = \frac{(x+4)+4}{x+4}$$

Then use the same trick you did.

That's pretty slick.

 

[Char. Limit]

That's pretty slick.

Thanks, it's my own little algebraic trick.

 

[Totalderiv]

Thanks for the help!

 

[HallsofIvy]

Thanks, it's my own little algebraic trick.

It is, of course, the same as the "polynomial division" that gb7nash suggested.

 

[Char. Limit]

It is, of course, the same as the "polynomial division" that gb7nash suggested.

Srsly? The way I learned polynomial division is much, much harder.

 

[Dick]

I think "much much harder" is a srs exaggeration.

 

[Char. Limit]

I think "much much harder" is a srs exaggeration.

Well I mean, I learned it the way long division is taught, and I never liked long division. I prefer my method, whether it's called polynomial division or not.

 

[Dick]

It is a way of doing polynomial long division. It works neat for linear/linear. But in that case polynomial long division isn't that hard either. Try it for (x^2+9)/(x+4). Sure, you can do it. At least polynomial long division is has a method instead of relying on a trick that you have to reinvent as the cases change.