(1+x)/(1-x)^3的不定积分,

Question

(1+x)/(1-x)^3的不定积分,

Answer 1

(1+x)/(1-x)^3=A/(1-x)^3+B/(1-x)^2+C/(1-X) [Cx^2+(-B-2C)x+(A+B+C)]/(1-x)^3=(1+x)/(1-x)^3 C=0 -B-2C=1 A+B+C=1 解得 A=2 B=-1 C=0 ∫(1+x)/(1-x)^3dx =∫[2/(1-x)^3-1/(1-x)^2]dx =-2∫(1-x)^(-3)d(1-x)+∫(1-x)^(-2)d(1-x) =(1-x)^(-2)-(1-x)^(-1)+C =1/(1-x)^2-1/(1-x)+C 如果有错请回信.