A complete record of all proceedings and testimony before the board at such hearing shall be taken down by a reporter appointed by the board. In case an action is brought to review any decision of the board, a transcript of such testimony, together with all exhibits or copies thereof introduced, together with the written request for hearing and other proceedings in the cause shall constitute the record on review; provided, however, that the board and other parties may stipulate in writing that a specified portion of the evidence be certified to the court for judgment and in such case the portion of the evidence specified and the stipulation specifying such evidence shall
be the record on review.