This paper presents a theory describing the dynamic nuclear polarization (DNP) process associated with an arbitrary frequency swept microwave pulse. The theory is utilized to explain the integrated solid effect (ISE) as well as the newly discovered stretched solid effect (SSE) and adiabatic solid effect (ASE). It is verified with experiments performed at 9.4 GHz (0.34 T) on single crystals of naphthalene doped with pentacene-d14. It is shown that the SSE and ASE can be more efficient than the ISE. Furthermore, the theory predicts that the efficiency of the SSE improves at high magnetic fields, where the EPR line width is small compared to the nuclear Larmor frequency. In addition, we show that the ISE, SSE, and ASE are based on similar physical principles and we suggest definitions to distinguish among them.