積分關於partial fraction?

1/(x^3 + x) = 1/x(x^2 + 1)
Let 1/x(x^2 + 1) = A/x + (Bx+C)/(x^2 + 1) = [A(x^2 + 1) + (Bx+C)x]/x(x^2 + 1)
=> 1 = Ax^2 + A + Bx^2 + Cx
=> 1 = (A+B)x^2 + Cx + A
Solving for A,B,C, we have A = 1, B = -1 and C = 0
Hence ∫1/(x^3 + x) dx = ∫1/x dx - ∫x/(x^2 + 1) dx
= ∫1/x - (1/2)∫1/(x^2 + 1) d(x^2 + 1)
= ln x - (1/2)ln(x^2 + 1) + C

2012-01-02 16:20:09 補充：
Rvy:
在HKCEE及HKALE的exam中, C不用寫得那麼清楚為constant. 詳情請參考HKCEE及HKALE的amaths, app maths 及 pure 的marking

圖片參考：http://s18.postimage.org/z6db305s7/daum_equation_1325408038233.png

最後答案如果你係用+C, 就要寫番where C is a constant

2012-01-01 16:57:56 補充：
s18.postimage.org/z6db305s7/daum_equation_1325408038233.png

2012-01-05 21:13:05 補充：
知識長
我當然有睇MARKING
第一, MARKING通常都係寫+constant
第2, MARKING就算用+C1, +C2 都會DEFINE 番
第3, http://lsforum.net/board/viewthread.php?tid=131649

最重要係, 數學唔係算術, pure更加注重表達
點解要靜係寫+C去冒呢個險?
而且, 你寫ln x, 如果個MARKER係嚴, 真係可以唔比A分你

partial fraction又唔係寫"全等"
我未見過任何一年既MARKING既LET PARTIAL FRACTION 寫"="