integration(7)

∫ln(3-x)dx

= xln(3-x)dx - ∫xd[ln(3-x)]

= xln(3-x)dx - ∫[-x/(3-x)]dx

= xln(3-x)dx - ∫[(3-x)/(3-x)]dx + ∫[3/(3-x)]dx

= xln(3-x)dx - ∫dx - 3∫[1/(3-x)]d(3-x)

= xln(3-x) - x - 3ln(3-x) + C

= (x-3)ln(3-x) - x + C

2011-01-16 11:32:30 補充：
Alternative method:
Use the rule of integration: ∫lnxdx = xlnx - x + C

∫ln(3-x)dx
= -∫ln(3-x)d(3-x)
= -[(3-x)ln(3-x) - (3-x) + C']
= -[(3-x)ln(3-x) + x - (3 - C')]
= (x-3)ln(3-x) - x + C

圖片參考：http://imgcld.yimg.com/8/n/HA00704496/o/701101160021213873369980.jpg


Hope I can help you!!!