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## Homework Statement

When I plug in

Integrate[ x/(1 + x), x]

into Mathematica, I get

x - Log[1 + x]

which I've been able to recreate on paper. However, when I plug in

Integrate[ 2 x/(1 + 2 x), x]

I get

1/2 + x - 1/2 Log[1 + 2 x]

but on paper I get

x - 1/2 Log[1 + 2 x]

My question is, where does the constant (1/2) come from? Is it me or Mathematica that's wrong?