Unfortunately, this is an area of English which may be slowly
undergoing a change. Not only do non-native speakers have
difficulty with it, but a surprising number of educated native speakers
seem to be using the inverted structure "incorrectly" more and
more. It is so prevalent that some books are calling it neither a
direct question nor an indirect question, but a semi-indirect question!
It is probably better to stick to the "correct" version until so many
people are doing it that the grammar experts finally give up and say
it's perfectly fine!
You will find, however, that native speakers usually generate the
"incorrect" form only when the indirect question is quite long --
almost never with indirect questions of very few words.
CJ