The area of the region enclosed by the curve y = 1/x + 1/(x+1), the lines x=1 and x=2 and the x-axis is the definite integral of y = 1/x + 1/(x + 1) between the limits x = 1 and x = 2.

Int[ y dx], x = 1 to x = 2

=> Int [ 1/x + 1/(x + 1) dx], x = 1 to x = 2

=> ln|x| + ln|x + 1|, x = 1 to x = 2

=> ln 2 + ln 3 - ln 1 - ln 2

=> ln 3 - ln 1

=> ln 3

**The required area is ln 3**

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