If Trump wanted an investigation of an American citizen the proper procedure would have been to ask the DOJ to investigate. Why didn’t he go to Bill Barr? If Barr wanted an investigation and he needed information from Ukraine he would ask his Ukrainian counterpart for help.
There are two reasons that Trump didn't do this.
1) He didn’t really want an investigation. He just wanted Zelensky to announce an investigation.
2) He knew that although it didn’t look great that Hunter Biden was hired by Burisma and was paid a lot of money, there was nothing illegal about it.