How to express integration $k$ times in a row?

Question

Differentiation can be expressed $k$ times in a row as either $f^{(k)}(x)$ or as $\frac{d^n}{dx^n}f(x)$. How do I express indefinite integration $k$ times in a row?

Answer 1

$$\underbrace{ \int\cdots\int }_k f(x) \; \underbrace{ \mathrm dx\cdots\mathrm dx }_k$$

but the lazy sometimes just use one $\int$.

Answer 2

A prior question: what do you mean by "integration $k$ times in a row"?

If you mean the sequence of functions $f_n$ given by $$\begin{align}f_0(x)&=f(x)\\ f_{n+1}(x)=\int_a^xf_n(t)\mathrm{d}t \end{align}$$ for some fixed value $a$, then in fact

$$f_n(x)=\frac{1}{(n-1)!}\int_a^x(x-t)^{n-1}f(t)\mathrm{d}t\text{,}$$ a result that motivates the definition of the Riemann–Liouville fractional integral $$I^{\nu}_af(x)\stackrel{\text{def}}{=}\frac{1}{(\nu-1)!}\int_a^x(x-t)^{\nu-1}f(t)\mathrm{d}t\text{.}$$ Unfortunately, there appears to be no consensus notation for the latter either (I've seen both $I$ and $J$ used, as well as $1$, $2$, or $3$ superscripts/subscripts).