这道题怎样凑微分,∫x/根号(x-3)dx请问这道题用凑微分法怎样做,

Question

这道题怎样凑微分,
∫ x/根号(x-3) dx
请问这道题用凑微分法怎样做,

Answer 1

∫ (x-3+3)dx/(x-3)^(1/2)=∫ (x-3)^(1/2)dx+3∫ dx/(x-3)^(1/2)
=∫ (x-3)^(1/2)d(x-3)+3∫ d(x-3)/(x-3)^(1/2)
=(2/3)(x-3)^(3/2) + 6(x-3)^(1/2) + C