17-20 Express the limit as a definite integral on the given interval. 17. $\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \frac{e^{x_{i}}}{1+x_{i}} \Delta x,[0,1]$

Step 1 ：The given limit is a Riemann sum for the function \(f(x) = \frac{e^{x}}{1+x}\) on the interval \([0,1]\).

Step 2 ：The limit of this sum as \(n\) approaches infinity is the definite integral of \(f(x)\) from 0 to 1.

Step 3 ：Therefore, we need to calculate the definite integral of \(f(x)\) from 0 to 1.

Step 4 ：The limit is expressed as the definite integral \(\int_{0}^{1} \frac{e^{x}}{1+x} dx\).