Question

求高数不定积分∫x/(1+x)^4dx

Answer 1

x/(1+x)^4 =(x+1-1)/(1+x)^4
=1/(1+x)^3 -1/(1+x)^4
所以∫x/(1+x)^4 dx
=∫1/(x+1)^3 dx -∫1/(x+1)^4 dx
=-1/2 (x+1)^(-2) +1/3 (x+1)^(-3) +c