求不定积分∫e的三次根号x幂dx
问题描述：
求不定积分∫e的三次根号x幂dx
答
设x^(1/3) = u
那么x = u^3
dx = 3u^2du
e^(x^(1/3))dx = 3u^2 e^u du
对这个积分得3 E^u (2 - 2 u + u^2)
代入x即可
答
z³ = x,dx = 3z² dz∫ e^[x^(1/3)] dx= 3∫ z²e^z dz = 3∫ z² de^z= 3z²e^z - 3∫ 2ze^z dz= 3z²e^z - 6∫ z de^z= 3z²e^z - 6ze^z + 6∫ e^z dz= 3z²e^z - 6ze^z + 6e^z ...