x乘以根号下x-2不定积分

题目

x乘以根号下x-2不定积分

答案

∫x√(x-2) dx,令u = x-2,du=dx
= ∫(u+2)√u du
= ∫u^(3/2) du + 2∫√u du
= (2/5)u^(5/2) + 2(2/3)u^(3/2) + C
= (2/15)(3x+4)(x-2)^(3/2) + C