帮忙做不定积分：∫sinxcos^3(x)e^(1-sin^2(x))dx

I = ∫sin(x)*cos^3(x)*(e^(1-sin^2(x)))*dx
= -∫cos^3(x)*(e^(cos^2(x)))*d(cos(x))
令t=cos(x)：
I = -∫(t^3)*(e^(t^2))dt
= -(1/2)*∫(t^2)*(e^(t^2))*d(t^2)
令s=t^2：
I = -(1/2)*∫s*(e^s)*ds
分部积分,得：
I = -(1/2)*s*(e^s)+(1/2)*(e^s)
将s=t^2=cos^2(x)代入,得：
I = -(1/2)*(cos^2(x))*(e^(cos^2(x)))+(1/2)*(e^(cos^2(x)))