Integration

[Deleted User]

Is the antiderivative of 4/(3x+6):

4/3*log|3x+6| + c

or

4/3*log|x+2| + c

[polar]

both, it'll be the c value that's different

[paulsterio]

note 1 - use ln, not log, log denotes the logarithm to the base 10, ln denotes the natural logarithm, the logarithm to the base e - make sure you get this right, it's either:

OR

Secondly, it's actually either because you can take out the factor as shown:





(log law: ln(ab) = ln(a) + ln(b))



So you can see that is a constant, so let's define that as

[availn]

That is the fun thing with logs, dilations in the x direction can be done with translations up.



The ln(3) is a constant, so it's just a part of c.