Oh I thought the result $\displaystyle (\ln 2)^2$ was from a book. (I must say, it's really good that you show your working

)

The problem in that is I don't know what log stands for, because it depends on the books !

So, assuming that this "log" is base 10, the answer is $\displaystyle \frac{(\ln 2)^2}{\ln(10)}+c$

If this "log" is the napierian (natural) logarithm, then the answer is simply $\displaystyle (\log 2)^2+c$

Your work is correct aside that. There's just the confusion log / ln that just affects the result.