\[\int_{0}^{x}e^{-t}I_{n}\left(t\right)\,\mathrm{d}t=xe^{-x}(I_{0}\left(x\right)%
+I_{1}\left(x\right))+n(e^{-x}I_{0}\left(x\right)-1)+2e^{-x}\sum_{k=1}^{n-1}(n%
-k)I_{k}\left(x\right),\]