Hi,
Just use Free form input, Solve with steps the integral of
x*(2*a^2)arccos(x/(2a))-(x^2/2)*sqrt(4a^2-x^2) over x
and you get the solution. You open then “Show all steps” and get all of them. It’s about 3-4 pages of steps… Mathematica provides you also with a Manipulate graph to see your function.