求不定积分x/(1-x)^3dx_数学解答

求不定积分x/(1-x)^3dx

人气：346 ℃　时间：2020-04-11 14:14:25

解答

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