Quick & Simple question - integration (1 Viewer)

[blackops23]

Hi guys, I'm having confusion over one particular thing, a lot of my integration questions, part of the answer is in the form of e.g. ln(3-4x), whereas my answer was ln(4x-3).

e.g this question from Coroneos:

integrate 1/(16-9x^2)

what I did was factor out the 1/(-9) so it I would have to integrate 1/(x^2 - (16/9)) and multiply that by -1/9. The answer I got was--> -1/24[ln(3x-4) - ln(4x+3)]

which = 1/24[ln(4x+3) - ln(3x-4)]

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However

Coroneos' answer was 1/24[ln(4+3x) - ln(4-3x)]

(i suppose he factored out 1/9 instead of -1/9, and he used the formula for integrating 1/(a^2 - x^2)

So are both answers right or am I wrong and Coroneos is in the right?

Help greatly appreciated, thanks

 

[K4M1N3]

Yes your answer is fine because logs actually have absolute value signs around linear logs ie it is ln|4-3x| which you will find is the same as ln|3x-4|

 

[Drongoski]

Note

Kamine is basically correct. But you must enclose the argument(s) of the log(s) in the absolute value sign.

 

[blackops23]

Yes your answer is fine because logs actually have absolute value signs around linear logs ie it is ln|4-3x| which you will find is the same as ln|3x-4|

ahh i see now thanks man