#3976 Integration Error

[Ahmed Sadek]

integrating log(x+1) should be (x+1)*log(x+1)-x according to integration by parts rule.

Maxima adds -1 to the equation .. which is not producible either by hand .. and/or using #wolframalpha with #mathematica behind it.

Source of Error:
I can also imagine that the source of error stemmed from the fact that some resources stated that ∫ln(x) dx = x ln(x) -x = x (ln(x) - 1)
by getting (x+1) as the parameter for x then (x+1) ln(x+1) - (x + 1) = (x+1) ln(x+1) - x - 1 <== the error appears.

[Stavros Macrakis]

Antiderivatives / integrals always have an arbitrary constant, usually denoted C.

That is, integrate(1,x) can be x or x+1 or x-1. All of those are correct, since D(x)=D(x+1)=D(x-1)=1.

[Ahmed Sadek]

Thank you Stavros .. I think I should get back to work on my fundamentals again.