How do you integrate $(x/(x+2))$ ?

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Answer 1 · 2016-05-29T16:11:57

$x-2lnabs(x+2)+C$

We can simplify this way is written:

$intx/(x+2)dx=int(x+2-2)/(x+2)dx=int((x+2)/(x+2)-2/(x+2)dx)$

$int(1-2/(x+2))dx=int1dx-2int1/(x+2)dx$

From here the integration is fairly simple:

$=x-2lnabs(x+2)+C$

How do you integrate (x/(x+2))(x/(x+2))?