I like to go jogging and to go swimming.和I like to go jogging and go swimming.請問哪個正確呢？

Both "jogging" and "swimming" can be a noun by itself, on top of the verbal forms (gerund and participle) of the verbs "jog" and "swim".
(1) as noun: I like to go jogging and swimming. (only single word)

(reduction of the compound sentence: I like to go jogging and I like to go swimming.)

(2) as gerund: I like jogging and swimming. (single word gerund)
I like jogging steadily up the hill and swimming across the harbor. (gerund phrase)

Additional: example of jogging and swimming used as participle
Jogging steadily up the hill, I saw you swimming slowly across the harbor.

I like jogging and swimming

"gerund" technical is a noun in the form of the present participle of a verb,eg:-go jogging in the sentence "I like go jogging", "I like jogging";"I like swimming"
Hence" I like go jogging and swimming."
"and" conjunction must be used to join two gerund phrases etc. referring to things that are related in some way in Sport.eg:-jogging and swimming.