Gramma

The first one "He is out to do sth." means that he is out now and he is doing sth outside.

The second one "He is going out" is meaningless because he must have already gone to do something, we can't say "is going out". Go out is a short action.

Actually both sentences are correct, but rely on the different situtations.

1.) He is out to do sth.
Meaning: He is not here and has gone outside already to do sth.

2.) He is going out to do sth.
Meaning: He is preparing to go out to do sth. OR He will go out to do sth.

Since " is going to " form can be regarded as a presentation of simple future tense.

Therefore, if some one is not here, sentence 1) should be used.

^O^ ^O^ ^O^