Question

求∫e^xcos2x不定积分

Answer 1

∫e^xcos2x=∫渗信cos2xde^x=e^xcos2x-∫e^xdcos2x=e^xcos2x+2∫sin2xde^x=e^xcos2x+2e^xsin2x-2∫e^xdsin2x=e^xcos2x+2e^xsin2x-4∫e^xcos2xdx所余饥以∫e^xcos2x=（e^xcos2x+2e^xsin2x）丛毁轮/5+C