Incorrect integral calculation in MuPAD

Integration of function x-1 wrt x using command int(x-1,x) in MuPAD gives answer as (x-1)^2/2 instead of x^2/2-x. Can anybody explain why?

Thanks in advance.

Regards Nishant

Answer 1

[Walter Roberson]

The difference between the two is 1/2 which is a constant and so falls into the usual "plus an arbitrary constant" category. If you diff((x-1)^2/2,x) you get x-1, so you cannot say that the result is incorrect.

[Nishant Shankhwar]

Your argument is correct, but in sympy or maple same integral comes out to be x^2/2-x and diff(x^2/2-x,x) is x-1. Therefore x^2/2-x seems more convincing than (x-1)^2/2.

[Walter Roberson]

x^2/2 - x might be more conventional but remember that the indefinite integral is really x^2/2 - x + a constant, so any result of the form x^2/2 - x + a particular constant + an implied constant is mathematically correct

It does look unusual, but the mathematics of it is sound.