Incorrect answer in indefinite integration (HP Prime)

02282024, 07:00 PM
Post: #1




Incorrect answer in indefinite integration (HP Prime)
integral(ln(x+2)dx
answer: x*ln(x+2)x+2*ln(x+2)2 why is there a 2 at the end? 

02292024, 08:55 AM
(This post was last modified: 02292024 09:50 AM by rkf.)
Post: #2




RE: Incorrect answer in indefinite integration (HP Prime)  
02292024, 02:25 PM
Post: #3




RE: Incorrect answer in indefinite integration (HP Prime)
I had the same thought. Was wondering how/why XCAS came up with a constant equaling 2 as opposed to something else!


02292024, 02:46 PM
Post: #4




RE: Incorrect answer in indefinite integration (HP Prime)
Maybe it is the airspeed velocity of an unladen African sparrow?


02292024, 03:42 PM
(This post was last modified: 02292024 03:55 PM by carey.)
Post: #5




RE: Incorrect answer in indefinite integration (HP Prime)  
02292024, 04:31 PM
Post: #6




RE: Incorrect answer in indefinite integration (HP Prime)
Why 2?
You can rewrite the answer x*ln(x+2)x+2*ln(x+2)2 as (x+2)*ln(x+2)(x+2). Prime G2, 15C CE 

02292024, 04:42 PM
Post: #7




RE: Incorrect answer in indefinite integration (HP Prime)
(02282024 07:00 PM)ReinXXL Wrote: why is there a 2 at the end? We can consider the singularity at \(x=2\) a natural lower bound of the definite integral. This choice of the integral constant makes it \(0\) at that value: \( \begin{align} F(x) &= \int_{2}^{x} \log(t+2) \; \mathrm{d}t \\ \\ &= (t+2) \log(t+2)  t \Big_{2}^x \\ \\ &= (x+2) \log(x+2)  x  2 \\ \end{align} \) 

02292024, 05:47 PM
Post: #8




RE: Incorrect answer in indefinite integration (HP Prime)
(02292024 03:42 PM)carey Wrote:(02292024 02:46 PM)KeithB Wrote: Maybe it is the airspeed velocity of an unladen African sparrow? Or flying West? Tom L Cui bono? 

02292024, 06:23 PM
Post: #9




RE: Incorrect answer in indefinite integration (HP Prime)
Not really mysterious, it's a linear change of variable.


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