1、∫xsin(x^2)cos3(x^2)dx ＝（1/2)∫sin(x^2)cos3(x^2)dx^2
=(1/4)∫[sin4(x^2)-sin2(x^2)]dx^2
=(1/4)[∫sin4(x^2)dx^2-∫sin2(x^2)dx^2]
令t=x^2,则
原式＝(1/4)[∫sin4tdt-∫sin2tdt]
=(1/4)[(1/4)∫sin4td4t-(1/2)∫sin2td2t]
＝（1/4)[(1/2)cos2t-(1/4)cos4t]
=(1/8)cos2(x^2)-(1/16)cos4(x^2)