求∫e∧x sinx∧2 dx的解题过程,

∫ e^x * sin²x dx= ∫ e^x * (1 - cos2x)/2 dx= (1/2)e^x - (1/2)NN = ∫ e^xcos2x dx = (1/2)∫ e^x d(sin2x)= (1/2)e^xsin2x - (1/2)∫ e^xsin2x dx= (1/2)e^xsin2x + (1/4)∫ e^x d(cos2x)= (1/2)e^xsin2x + (1/4)e^xcos2x - (1/4)N(5/4)N = (1/4)(2sin2x + cos2x)e^xN = (1/5)(2sin2x + cos2x)e^x + C原式 = (1/2)e^x - (1/5)e^xsin2x - (1/10)e^xcos2x + C