Question

ln(1-x)求它的积分

Answer 1

∫ln(1-x)dx

=-∫ln(1-x)d(1-x)

=(x-1)ln(1-x)+∫-(1-x)dx/(1-x)

=(x-1)ln(1-x)-∫dx

=(x-1)ln(1-x)-x +C

不定积分的公仔戚式：

1、∫ a dx = ax + C，a和C都念桥陵是常数

2、∫ x^a dx = [x^(a + 1)]/(a + 1) + C，其中a为常数且 a ≠消宴 -1

3、∫ 1/x dx = ln|x| + C

4、∫ a^x dx = (1/lna)a^x + C，其中a > 0 且 a ≠ 1

5、∫ e^x dx = e^x + C

6、∫ cosx dx = sinx + C

7、∫ sinx dx = - cosx + C

8、∫ cotx dx = ln|sinx| + C = - ln|cscx| + C

Answer 2

ln(1-x)的知搭积搭耐拿分：亩悔

Answer 3

∫渗好含丛笑袜燃ln(1-x)dx
=-∫ln(1-x)d(1-x)
=(x-1)ln(1-x)+∫-(1-x)dx/(1-x)
=(x-1)ln(1-x)-∫dx
=(x-1)ln(1-x)-x +C