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Some integrals and integral transformations of a lightning pulse function useful for lightning discharge modeling are presented in this paper. The integral of the new channel-base current function (NCBC), the integral of the square of this function, its Laplace transform and Fourier transform are calculated analytically. Some results are compared to the results from literature for the Heidler's lightning channel-base function. These integrals of pulse functions are used in analytical calculations of lightning electromagnetic field (LEMF) and the results are presented in the paper. It makes the NCBC function suitable for computations of lightning induced effects.