The "to infinitive", in that example, is a noun phrase; a gerund is a noun, and a noun is a noun. So they are all the same. So they are all the same. Only one question mark is used in English, and there is no space between between words and punctuation.You must use a prepositional phrase instead, such as “go ‘on a trip’”. Once again, the simple explanation is because ‘trip’ is an inherent noun in this case (as opposed to the verb, ‘to trip’), whereas ‘swimming’ is a ‘created’ noun, a gerund. In light of that, a somewhat related area of confusion is “I am going crazy.”.
See my answer to the duplicate regarding this not actually being a gerund, but the present participle. The short answer is that it is possible to use both, but the infinitive is far more natural, whereas using a gerund after want has an air of "business-speak" or "managementese" I would personally try to avoid.
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