How do we denote the nth antiderivative of a function?
Given that we have some function, say #f(x)=5x^3+3x^2-3# , the first derivative would be denoted as #f'(x)=15x^2+6x# or #f^1(x)# ...
I know the first antiderivative of #f(x)# would be written as #F(x)# . But do we have anything to show the second and third antiderivatives?
Given that we have some function, say
I know the first antiderivative of
1 Answer
Capitalization, going from function
Explanation:
In some treatments (for example Calculus by James Stewart) , there is a difference between the "most general antiderivative" and "the indefinite integral".
I am not aware of a standard notation for the such 'higher' antiderivatives.
For integrals, we use
and the we can (if we wish) repeat:
If you are interested in exploring 'higher order' antiderivatives, I suggest the notation
With this notation you have