The phrase "various books" is correct and can be used in written English. It is often used when mentioning several books of different types or genres. For example, "She enjoys reading various books, including novels, biographies, and non-fiction works.".
Various books are used as case studies.
I have various books that mean a lot to me.
He has written various books on history and journalism.
They write in passing about their families, their travels, various books and films, their own novels.
Reading various books at once is sort of like doing an enjoyable Stations of the Cross.
Librarians challenge them to create projects based on various books and their themes.
Writer tells about the history of this question, and the various books on the subject.
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Software Engineer at Adobe, UK