MATLAB: The answer this trigonometric integration example is wrong despite attempts to remedy it. Anyone knows why

Question

Answer 1

It is the correct result, it is just a different way of writing it.

>> syms x
>> f = 2*cos(x) + sin(x)
f =
2*cos(x) + sin(x)
>> int_f = int(f)
int_f =
-2*cos(x/2)*(cos(x/2) - 2*sin(x/2))
>> simplify(diff(int_f)) % same expression back
ans =
2*cos(x) + sin(x)