Which kernel to use for data in [0;1]?

I need to learn density f(x):[0..1]->[0..1]
In particular, x's are values generated by some unknown probability
model.
How would I do kernel density estimation in this setting?

I had an idea to log-transform the data, make it symmetric around x=0
by reflection, and use Gaussian kernel. Is this a typical approach to
use in this setting?

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