Question

CALCULUS - NATURAL LOG INTEGRATION

Answer 1

What's your question?

Answer 2

Integration of x^2 - 4 / x

Sorry I'm the worse library ever. Can't even load a google search on this wifi so I had to use my phone

Answer 3

Integration symbol is the big the big S. I need to use substitution on this one, so far I got this:

Let u=x^2-4
Let du=2xdx
1/2du=xdx

Therefore

Integration of u/du

Answer 4

Are there limits to this integral?

Answer 5

I'm not sure of how to continue. If it was du/u then I would do Ln |u| +C

Answer 6

No limits

Answer 7

Okay, then the absolute values are mandatory.

Is it (x^2 - 4)/x or x^2 - (4/x)?

Answer 8

(X^2 - 4)/x

Answer 9

Please simplify to x - (4/x) and proceed.

Answer 10

so i split them up into x^2/2 - 4/x and therefore x - (4/x) ?

Answer 11

That is a convenient way to proceed, yes.

Answer 12

\[\frac{ x^2 }{ x }-\frac{ 4 }{ x } = x-\frac{ 4 }{ x }\]

Answer 13

ok just making sure

Answer 14

Right. We had a goofy "2" up above, but you have fixed it.

Answer 15

cool. but now im even more lost. what should i substitute u for?

Answer 16

If you need to substitute, feel free. I'm not sure why you would want to do that. Tackle each piece separately and just write down the answer.

Answer 17

\(\int x - \dfrac{4}{x}\;dx = \int x\;dx - \int \dfrac{4}{x}\;dx\)

Answer 18

okay so the first integration would be \[\frac{ x^2 }{ 2 }\]

Answer 19

what about 4/x?

Answer 20

So far. We can worry about he arbitrary constant when we get to the end of all the terms.

4/x is why this problem is under "Natural Log Integration". Do it!

Answer 21

oh i see! sorry the wifi is so slow is taking up all my attention. give me a second to do it

Answer 22

\[\frac{ x^2 }{ 2 }-4\ln |x|+c\]

Answer 23

THAT, is perfect. Good work.

Answer 24

thanks! i was pulling my hair trying to figure out what to substitute lol

Answer 25

haha. Yeah, don't do that. :-)

Answer 26

thanks!