Find a formula for a higher degree antiderivative

[DXDeidara]

The problem asks to find a formula for a higher degree antiderivative. This formula pattern is similar to the one stated in the Fundamental Theorem of Calculus: F(X)=∫f(t)dt.

Fn(x)=∫*F(t)dt, with certain expression in the asterisk.

 

[HallsofIvy]

I really don't understand what you are asking.

 

[JJacquelin]

The problem asks to find a formula for a higher degree antiderivative. This formula pattern is similar to the one stated in the Fundamental Theorem of Calculus: F(X)=∫f(t)dt.
Fn(x)=∫*F(t)dt, with certain expression in the asterisk.

I suppose that DXDeidara claims for a formalism in order to generalize the antiderivatives of higer degree (multiple integrals)
This formalism already exists in a more general background of differintegration: considering not only integer degrees, but also non integer degrees (positive or negative).
For example, see the notation page 2 (§.3) and page 3 (§.5) in the paper :
"La dérivation fractionnaire" (i.e. fractionnal calculus)
http://www.scribd.com/JJacquelin/documents
More relevant references are provided page 5, especially ref.[1]
Here, in attachment, the degree μ for antiderivatives or -μ for derivatives, can be any real number. So, the particular case of integer μ is included.