Thread: Integrate (1 + 3x)(x - 2)

1. Integrate (1 + 3x)(x - 2)

Evaluate this integral

$\int\((1+3x)(x-2) dx$

I use the general power formula for this one.

Let u = (1+3x)(x-2)
du = 6x-5

I stop from here, I don't know what's next and I don't know if I do it right.

2. What did you do exacly?

Expand what you have in brackets and integrate as usual.

3. Originally Posted by jasonlewiz
Evaluate this integral

$\int\((1+3x)(x-2) dx$

I use the general power formula for this one.

Let u = (1+3x)(x-2)
du = 6x-5

I stop from here, I don't know what's next and I don't know if I do it right.

Sorry for the title/subject, I forgot to edit
$\int\((1+3x)(x-2) dx = \int\((3x^2 - 5x - 2)dx$...

It's strange that you would "know" u-substitution, but not how to FOIL and integrate a polynomial term by term...

4. Originally Posted by TheChaz
$\int\((1+3x)(x-2) dx = \int\((3x^2 - 5x - 2)dx$...

It's strange that you would "know" u-substitution, but not how to FOIL and integrate a polynomial term by term...

ahh, so I can change (1+3x)(x-2) to (3x+1)(x-2) ^^now I know..thanks

5. That's not the point!

You expand the brackets like this:

$(1+3x)(x-2) = 3x^2 - 5x - 2$

Then you integrate:

$\displaystyle \int 3x^2 - 5x - 2\ dx$