The dynamic magnetic susceptibility of magnetic materials near ferromagnetic resonance (FMR) is very important in interpreting dc-voltage obtained in an electrical detection of FMR. Based on the causality principle and the assumption that the usual microwave absorption lineshape around FMR is Lorentzian, general forms of dynamic magnetic susceptibility of an arbitrary sample and the corresponding dc-voltage lineshapes of the electrical detection of FMR are obtained. Our main findings are: 1) The dynamic magnetic susceptibility is not a Polder tensor for a material with an arbitrary magnetic anisotropy. Two off-diagonal matrix elements of the tensor near FMR are not in general opposite to each other. However, the linear response coefficient of the magnetization to the total radio frequency (rf) field (sum of the applied external rf field and the internal rf field due to the precessing magnetization, a quantity cannot be measured directly) is a Polder tensor. This may explain why two off-diagonal susceptibility matrix elements are always assumed to be opposite to each other in analyses.2) The frequency dependence of dynamic magnetic susceptibility near FMR is fully characterized by six real numbers while its field dependence is fully characterized by seven real numbers. 3) A recipe of how to determine these numbers by standard microwave absorption measurements for a sample with an arbitrary magnetic anisotropy is proposed. Our results allow one to unambiguously separate the contribution of the anisotropic magnetoresistance to dc-voltage signals from that of the anomalous Hall effect. With these results, one can reliably extract the information of spin pumping and the inverse spin Hall effect, and determine the spin-Hall angle. 4) The field-dependence of the susceptibility matrix elements at a fixed microwave frequency may have several peaks when the effective magnetic field is not a monotonic function of the applied magnetic field. In contrast, the frequency-dependence of the susceptibility matrix elements at a fixed applied magnetic field has only one FMR peak. Furthermore, in the case that resonance frequency is not sensitive to the externally applied static magnetic field, the field dependence of matrix elements of the dynamic magnetic susceptibility, as well as dc-voltage, may have another non-resonance broad peak. Thus, one should be careful in interpreting observed peaks.