[填空题]
The following diagram shows th od+1mmlcf+s -e graph of wk*4 m*,bgs mo+e4gza f(x)=$\frac{4 x}{x^{2}+1}$ , for $0 \leq x \leq 6$ , and the line x=6 .
Let R be the region enclosed by the graph of f , the x -axis and the line x=6 .
1. Show that $\int f(x) \mathrm{d} x=2 \ln \left(x^{2}+1\right)+C$ .
2. The exact value for the area of the region R is $\ln k$ , where k is a positive integer. Find the value of k is .
