Gerund after "to". Sentence: We use music to helping us relax

I found this question in a test: "We use music to helping us relax." Where helping was the correct answer option. I want to know why is this form of the verb correct and not the infinitive one (help).


We use music to help us relax. We use music for helping us to relax. We use music for the purpose of helping us to relax. But your example with “to helping” is weird, and probably wrong to most readers here. I have not heard such a construct in seven decades of educated English usage, nor in idiom nor in slang.