Integrate question

[DrD]

[CAS]
a:=int(cos(2*x)^3*sin(2*x)^5,x); // From the original example, [CAS] var a becomes: -3*cos(2*x)^8+8*cos(2*x)^6-6*cos(2*x)^4)/48
b:=-(3*sin(2*x)^8-4*sin(2*x)^6)/48; // result obtained by hand, (and wxMaxima)

Testing for equivalency:
a-b; // -1/48, The constant that shows up within the [CAS] result.

I understand that the value stored in (var a) gets rewritten, but that -1/48 term makes comparing results troublesome.

1. How can a student learn to feel confident with this outcome?
2. How can real world automation applications reliably use this result? (In other words, an automatic process of some sort, that dynamically uses a computed result for control purposes).