They write it IN the book. They write it ON the page.

If you are talking about the contents of the book, then it is IN the book. If you want to refer to a specific page of the book then it is ON the page, or ON that page. You can write notes IN your book, but you write ON the cover of a book. You need to have a look at and practice your prepositions of place.

If you are saying 'books' (plural rather than singular 'book'), then you don't need the word 'the', just "They write about animals in books". 'The' refers to one specific book.