From the OP's formulation, I understand that the signal is represented in the frequency domain, possibly without explicit time-domain expression. The Fourier transform diagonalizes linear operators, and integration is an integral operator. For more details, Fourier transform diagonalizes the convolution operator.
In other words, instead of using of convolutive form in time, you using a product form, easier to implement, which applies pointwise, separately to each frequency. It can also be faster using the Fast Fourier transform.
So for each integration, each frequency component $F(\omega)$ is multiplied by $1/(j\omega)$. Or when dealing with amplitude, frequency component $|F(\omega)|$ is just multiplied by $1/|\omega|$. What is especially nice is that pointwise products gather. If you want to perform two integration steps, you just have to multiply by $1/(j\omega)\times 1/(j\omega)$ or $-1/(\omega^2)$, and so on for multiple integration, the reason for the $n$ power.
What you should take care of is the singularity at $\omega =0$. Formally, an integral of a function with a non-zero average diverges. So this Fourier integration is often performed with some windowing to take care of very low or very high frequencies.
You can find Matlab implementations at MatlabCentral: