I tried using the free input to show me how to integrate the following integral but it didn't show me the steps.
Solve with steps the integral of x*(2*a^2)*arccos(x/(2*a))-(x^2/2)*sqrt(4a^2-x^2) in the interval [0,a]
How to make Mathematica show me the steps?
It is interesting that it won't show steps for the definite integral, but if you ask free form for a definite integral it works just fine.
Solve with steps the integral of x*(2*a^2)*arccos(x/(2*a))-(x^2/2)*sqrt(4a^2-x^2) over x
That doesn't answer your question, but at least you can see the step by step solution before you plug in the limits.
Just use Free form input, Solve with steps the integral of \
x(2a^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.