\[\int_{0}^{x}e^{\pm t}t^{\nu}K_{\nu}\left(t\right)\,\mathrm{d}t=\frac{e^{\pm x}%
x^{\nu+1}}{2\nu+1}(K_{\nu}\left(x\right)\pm K_{\nu+1}\left(x\right))\mp\frac{2%
^{\nu}\Gamma\left(\nu+1\right)}{2\nu+1},\]