考試的 Integration question

(2+x)/(3√x+2) +x??

2009-07-10 14:43:47 補充：
As follows:

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Let 3sqrt x + 2 = u........(1) that is sqrt x = (u - 2)/3
(3/2sqrt x )dx = du
dx = (2 sqrt x du)/3
= 2(u -2)du/9...................(2)
x = (u - 2)^2/9
so 2 + x = 2 + (u -2)^2/9 = [18 + (u - 2)^2]/9 = (u^2 - 4u + 22)/9.....(3)
Using (1), (2) and (3) and neglect the x in the integral for the time being,
S (2 + x)dx/(3 sqrt x + 2)
= S [(u^2 - 4u + 22)/9][2(u - 2)du/9](1/u)
= (2/81) S (u^2 - 4u + 22)(u - 2)du/u
= (2/81) S (u^3 - 2u^2 - 4u^2 + 8u + 22u - 44)du/u
= (2/81) S (u^2 - 6u + 30 - 44/u)du
= (2/81) [ u^3/3 - 3u^2 + 30u - 44 ln u] + C
so substitute back (1) into the answer and add back S x dx will be the final answer.

yes, any ideas or solving method on this question?? thz