What is the symbolic condensed version of Equation 2?

[Orion1]

Equation1:
\frac{d^2}{dx^2} (x^n) = \frac{d}{dx} \left[ \frac{d}{dx} (x^n) \right]

The LHS for Equation1 is the symbolic condensed version for the RHS, however, what is the LHS symbolic condensed version for Equation2 RHS?

Equation2:
\text{?} = \int \left[ \int \left( x^n dx \right) \right] \; dx

 

[Maxos]

\int dx \int \left( x^n dx \right)

 

[Orion1]

\int dx \int \left( x^n dx \right)

Interesting, I have never seen that version before. I was expecting something as:
\int \int x^n dx dx = \int \left[ \int \left( x^n dx \right) \right] \; dx

However, what if I wanted to demonstrate an equation that must be integrated 10 times or even 100 times? Surely there must be a shorthand version?

 

[Hurkyl]

It's somewhat rare to see iterated indefinite integrals: generally you would specify bounds, even if it's something like:

<br /> \int_0^x \int_0^t f(s) \, ds \, dt<br />

I've often seen high dimensional integrals written something like:

<br /> \iint \cdots \int f(x_1, \ldots \, x_n) \, dx_1 \, dx_2 \, \cdots \, dx_n<br />

with some additional text indicating the region of integration... or instead written as a single integral whose dummy variable ranges over a high-dimensional space.


Another option, which I suspect is the best one for you, is to define an integral operator. For example, you could define the operator I via:

(If)(x) := \int_0^x f(t) \, dt

and then you could indicate an iterated integral by I^nf.

 

[iNCREDiBLE]

You can write D^{-2}f(x) and/or D^{-2}(x^n).