此结果是x²在积分号的上面,0在下面的结果
若相反,请加负号
Φ(x)=(ʃ2 x^2)e^tcostdt
=(ʃ2 x^2)e^tdsint
=e^t*sint(x^2,0)-(ʃ2 x^2)e^t*sintdt
=e^t*sint(x^2,0)+(ʃ2 x^2)e^tdcost
=e^t*sint(x^2,0)+e^t*cost(x^2,0)
-(ʃ2 x^2)e^tcostdt
∴Φ(x)=(ʃ2 x^2)e^tcostdt=1/2(e^t*sint(x^2,0)+cost*e^t(x^2,0))
=1/2[e^(x^2)*sin(x^2)+e^(x^2)*cos(x^2)-1]
Φ(x)’=xe^(x^2)*sin(x^2)+xe^(x^2)*cos(x^2)
+xe^(x^2)*cos(x^2)-xe^(x^2)*sin(x^2)
=2xe^(x^2)*cos(x^2)