求∫e^(x^1/3) dx 用分部积分法做如题

来源：学生作业帮助网编辑：六六作业网时间：2024/11/28 23:11:21

求∫e^(x^1/3)dx用分部积分法做如题求∫e^(x^1/3)dx用分部积分法做如题求∫e^(x^1/3)dx用分部积分法做如题设t=x^(1/3),x=t^3,dx=3t^2dt,原式=∫e^t

求∫e^(x^1/3) dx 用分部积分法做如题
求∫e^(x^1/3) dx 用分部积分法做
如题

求∫e^(x^1/3) dx 用分部积分法做如题
设t=x^(1/3),x=t^3,
dx=3t^2dt,
原式=∫e^t*3t^2dt
=3(t^2e^t-2∫t*e^tdt)
=3[t^2*e^t-2(te^t-∫e^tdt)]
=3t^2*e^t-6te^t+6e^t+C
=3x^(2/3)e^[x^(1/3)]-6x^(1/3)e^[x^(1/3)]+6e^[x^(1/3)]+C.