Question

Evaluate:

anti-deriviative

3/(x-4) dx

will I use U substitute

Answer 1

Yes.

Answer 2

Identify your composite functions f(a) and g(x) such that 3/(x-4) = f(g(x))

Answer 3

u= x-4
du= 1

Answer 4

Yes.

Answer 5

Well, actually not quite

Answer 6

du = 1dx

Answer 7

yes I had that just forgot to type it

Answer 8

ok good.

Answer 9

ok this is where I have trouble.....will it be 3/u ???? Doesn't look right

Answer 10

That is exactly right.

If u = x-4 then 3/(x-4) = 3/u

Answer 11

so will I add 1 to the u (exponent) to be u^2

Answer 12

Not quite. realize that you basically have \[3 * \frac{1}{u}\]
So the derivative of what function of u gives you \(\frac{1}{u}\)?

Answer 13

u^-1 ??

Answer 14

1/u is u^-1

Answer 15

So it's not that. \(\frac{d}{du}[ln\ u] = \frac{1}{u}\) remember?

Answer 16

not sure what you mean about that?

Answer 17

The derivative of ln x = 1/x right?

Answer 18

ln is the natural logarithm function.

Answer 19

oh, yes it does. Too many rules.....

Answer 20

yeah, you'll get them with practice.

Answer 21

So the anti derivative of 1/x = ln x + C

Answer 22

So 3 times the anti derivative of 1/u du = ?

Answer 23

ok lost again.....
I know we have 3/u or 3 * 1/u
would it be 3lnx + c ???

Answer 24

It would be 3(ln u) + C, but then you have to plug in what u is.

Answer 25

how about
3 ln\[\left| x-4 \right|\] + C

sorry couln't get them all in one line

Answer 26

Yep, that's it exactly.

Answer 27

I am getting there......slowly.......
Thanks I really appreciate your help.

Answer 28

Of course! Just keep practicing. You're doing very well

Answer 29

I have a test next Tue. So I will be asking questions up until then. I am sure I will talk to you again..

Answer 30

ok!

Answer 31

I got really good with the derivatives, so my brain still wants to do them.

Answer 32

Yeah, I know the feeling. Soon you'll get the hang of going the other way.

Answer 33

I will start one more question before I have to leave

Answer 34

ok