Problem 1405 (difficulty: 4/10)

Which of the following vector fields are gradient fields? For those that are not give a closed curve on which the line integral of the field does not vanish.

\(\displaystyle (\ch y; x\sh y) \qquad (\ch x; y\sh x) \qquad \left(\frac{x}{x^2+y^2};\frac{y}{x^2+y^2};\right) \)

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