Problem

甲、填充題：共 8 題，每題 8 分，共 64 分。請在答案卷上列出題號依序作答。

7. Find the work done by the force $\mathbf{F}=\dfrac{x\mathbf{i}+y\mathbf{j}}{(x^2+y^2)^{3/2}}$ over the plane curve $\mathbf{r}(t)=(e^t\cos t)\mathbf{i}+(e^t\sin t)\mathbf{j}$ from the point $(1,0)$ to the point $(e^{2\pi},0)$. Answer : \underline{\quad(1)\quad}