The integrals in Gradshteyn and Ryzhik. Part 11: The incomplete beta   function
  The table of Gradshteyn and Ryzhik contains some integrals that can be expressed in terms of the incomplete beta function. We describe some elementary properties of this function and use them to check some of the formulas in the mentioned table. 
Khristo Boyadzhiev, Luis Medina and Victor Moll