How can I integrate these two challenging expressions?

[Joza]

I need help on these two integration questions:

1.

(x^2 -16)/(2x + 8) dx


2.

1/(1+9x^2) dx


I can't seem to find a "u" for either. And I tried a tan identity on number 2 to no avail.

 

[Office_Shredder]

Did you try factoring the first one?

 

[Joza]

OH WAIT...

Yea so x^2 - 16 would be (x + 4)(x - 4).

Then I can pull a 1/2 outside, and I'll be left with (x + 4) on the bottom. That will cancel out, so it will be the integral of (x - 4)?

 

[HallsofIvy]

Well, because of that 1/2 you "pulled outside", it will be (1/2) the integral of x-4.

As far as the second is concerned, you might try letting u= 3x and then think about the derivative of arctan u.

 

[Joza]

Yea that's what I meant.

Well I tried using 1/(1^2 + (3x)^2)...but that didnt work.