Prove standard cauchy distribution isn't part of exponential family.

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So the density is:

$$f(x) = \frac{1}{\pi(1+x^2)}$$

and I am supposed to prove this standard Cauchy distribution isn't part of the exponential family. I assume the best way to go about this would be to show a contradiction via one of the properties of members of the family but I haven't been able to do that.

Would appreciate a push in the right direction!