integration question

[jaesen]

if i had ∫1/(3x+3) dx
would the answer be (1/3) ln | 3x + 3 | or would it be (1/3) ln | x + 1 | ?

[brightsky]

The former.

[jaesen]

The former.

care to explain why it's not the first one? if you use substitution, you get the first one. ;(

[m@tty]

Differentating both gives the required result, so they are both correct anti-derivatives.






The reason it can be either is outlined below:




And since is simply another constant

can equal .

Thus proving beyond doubt that they are both correct, and the reason behind this...

[jaesen]

Differentating both gives the required result, so they are both correct anti-derivatives.






The reason it can be either is outlined below:




And since is simply another constant

it can equal .

what about when doing definite integrals? they both give different answers

[m@tty]

They shouldn't give different answers - try again.

[jaesen]

the thing is, when doing the definite integrals, the constant isn't there. so now what?

It's cool. i've discovered that the 3 cancels out

[m@tty]

I'll show you.

Prove:















See?

Anyway, the important fact is that you can still pull the constant of out, by logarithm laws. So both methods yield the same answer.

[m@tty]

It's cool. i've discovered that the 3 cancels out

Great. Glad I could help.