Ok, so let's assume we have the function f(x).

If we want to find the derivative, we write f'(x). If we want to find the derivative of this as well, we write f''(x), right?

Now, let's go back to f(x). If we want to integrate this, we write F(x). Now, if we want to integrate F(x) again, how do we write this?

2. Define a function $g(x)$ such that $\frac{d^2(g(x))}{dx^2} = f(x)$

3. Originally Posted by No Logic Sense
Ok, so let's assume we have the function f(x).

If we want to find the derivative, we write f'(x). If we want to find the derivative of this as well, we write f''(x), right?

Now, let's go back to f(x). If we want to integrate this, we write F(x). Now, if we want to integrate F(x) again, how do we write this?
One way to write it would be $\int^x \int^y f(t)dt dy$.
Some authors use $f^{(n)}$ to mean the "nth derivative" and then use $f^{(-n)}$ for the "nth integral". You will also see $D_n f$ and $D_{-n} f$ for those.

Of course, $f^(0)$, $f^0$, and $D_0 f$ are just f itself.