Question

how do I find the antiderivative of 2/x?

Answer 1

\[2 \int\limits \frac{dx}{x} = 2\ln(x) +c\]

Answer 2

where do you get c?

Answer 3

because this is an indefinite integral, u must add a constant at the end of every indefinite integral

Answer 4

the see come if u want to understand the proof in depth from Taylor series, and from integral definition, combined with differentiation definition

Answer 5

this is where the c comes from as i mentioned above, also some numerical integral methods can show this fact as well, whichever way u prefer to visualize the concept.

Answer 6

You could expand it a little. Because 2/x also accepts negative numbers, and ln(x) does not: \[\int\limits \frac{2}{x}dx= 2 \int\limits \frac{1}{x}dx= 2 \ln|x|+C\]which allows negative numbers to join in!

Answer 7

hmm, I still don't get how to find C, but I have some terms to search for :)

Answer 8

yes negative numbers are undefined that's why we ignore the absolute structure because its an axiom to mathematician....

Answer 9

you have add c at every indefinite integral take that for granted

Answer 10

you have to*

Answer 11

We cannot ignore the negative numbers is we have to evaluate:\[\int\limits_{-2}^{-1} \frac{1}{x}dx\]

Answer 12

because if ln(x) +c and want to differentiate that would be different from differentiating ln(x) with no constant i hope this helps

Answer 13

we are talking about indefinite integral not definite integral

Answer 14

as i said the world of mathematician is different

Answer 15

hmm, as an example, how would you go about finding c when f(x) = 2 / x ?

Answer 16

mathematicians

Answer 17

u have to have some initial values provided in the question to find c, this is called in general IVP, Initial Value Problem

Answer 18

hmm, I see. allright, I've got reading to do. Thanks for your help :)

Answer 19

if u want i can prove to u how the c comes into the integral but i am worried that u get confused

Answer 20

I'm confused enough, thanks ;)

Answer 21

hehehehe good luck, it is good to be confused some times you know...

Answer 22

have u done differential equations yet?