AUSTIN, Tex. — Texas’ State Board of Education has approved new history textbooks, but only after defeating six and seeing a top publisher withdraw a seventh — capping months of outcry over lessons that some academics say exaggerate the influence of Moses in American democracy and negatively portray Muslims.

The board on Friday approved 89 books and classroom software packages that more than five million public school students will begin using next fall. But it took hours of sometimes testy discussion and left publishers scrambling to make hundreds of last-minute edits, some to no avail. A proposal to delay the vote to allow the board and general public to better check those changes was defeated. “I’m comfortable enough that these books have been reviewed by many, many people,” said Thomas Ratliff, a Republican and the board’s vice chairman. “They are not perfect. They never will be.”

The history, social studies and government textbooks were submitted for approval this summer, and academics and activists on the right and left criticized many of them. Some worried that the textbooks were too sympathetic to Islam or played down the achievements of President Ronald Reagan. Others said they overstated the importance of Moses to America’s founding fathers or trumpeted the free-market system too much.

Bitter ideological disputes over what is taught in Texas classrooms have for years attracted national attention. The new books follow the state academic curriculum adopted in 2010, when Republicans on the board approved standards including conservative-championed topics like Moses and his influence on systems of law. They said those would counter what they saw as liberal biases in classrooms.