a log-linear Interpolation can be calculated by the MKL data fitting if one applies the toolbox to the log-scaled values and applied the exponential function to the result of dfdInterpolate1D.
What about the Integration? One has to apply the exponential function on each integration segment. My first idea was to use the call back mechanism of dfdIntegrateEx1D.
If I understand correctly I has to implement the integration by my-self. It is not a big deal, but at least performance improvements for the integration parts seems to reduce to managed code performance (I apply a .net wrapper for the MKL functionality and the call back method is managed code as well).