Integrate[(4 x)/(2 x + 1), x]
1 + 2 x - Log[1 + 2 x]
Notice the extra
1. The answer should be
2 x - Log[1 + 2 x] plus the constant of integration. But Integrate never gives a constant of integration.
Integrate[4 x, x] (2 x^2*)
Actually, here is the answer by Rubi:
Int[(4 x)/(2 x + 1), x] (* 2 x - Log[1 + 2 x] *)
And by Maple
and by Wolfram Alpha
I restarted the kernel, restarted Mathematica. Same answer. Using V 9.01 on windows 7.
Any idea what is going on? Is this a known feature/issue? One can of course argue that the answer is not wrong, since the constant of integration can be any value, but it is strange that it shows up here only, and with a specific value.