Expectation of Random Variable with even Probability Density Function

By Definition of Expectation of Random Variable:

$$ E(X)= \int_{-\infty}^{\infty}\,x\,f_X(x)\,dx $$

Now if the pdf $f_X(x)$ is Even we know that $E(X)=0$ (Ofcourse if integral Converges, i.e, Lets exclude cases like Cauchy Random Variable)

Is the Converse True, i.e., is there a Random Variable $X$ whose pdf is Neither Even-Nor Odd, such that $E(X)=0$.