Is wolfram alpha giving me the right answer?

Questions
,
1

this is my input: “integral of 3/x + 2/(x-2) - 1/(x+2)”

all the steps look good until after the last step where it gives the answer. it changes 2log(x-2) to 2log(2-x)

2

The easiest way to check this is probably to calculate the derivative of the solution that WolframAlpha gives:

D[2 Log[2 - x] + 3 Log[x] - Log[2 + x], x]

(*-(2/(2 - x)) + 3/x - 1/(2 + x)*)

This is identical to the integrand:

Simplify[3/x + 2/(x - 2) - 1/(x + 2)==-(2/(2 - x)) + 3/x - 1/(2 + x)]

(*True*)

Cheers,

M.