求∫（0,1）x*(1-x)^2)/(1+x)^2dx+∫（0,1)x^3*(1-x)^2/(1+x)^2dx的积分,

∫x(1-x)^2dx/(1+x)^2
=∫x[(1+x)^2-4x-4+4]dx/(1+x)^2
=∫xdx-4∫dx/(1+x)+4∫dx/(1+x)^2
=(1/2)x^2-4ln|x+1|-4/(1+x)+C
∫x^3(1-x)^2dx/(1+x)^2
=∫x^3[(1+x)^2-4x-4+4]dx/(1+x)^2
=∫x^3dx-4∫x^3dx/(1+x)+4∫x^3dx/(1+x)^2
< x^3/(1+x)=(x^3+1-1)/(1+x)=(x^2-x+1)-1/(1+x)
x^3/(1+x)^2=(x^2-x+1)/(x+1)-1/(1+x)^2=[(x+1)^2-3x-3+3]/(x+1)-1/(1+x)^2
=x-2+3/(x+1)-1/(1+x)^2
=(1/4)x^4-4∫(x^2-x+1)dx-4∫dx/(1+x)+ 4∫(x-2)dx+12∫dx/(1+x)-4∫dx/(1+x)^2
=(1/4)x^4-(4/3)x^3+4x^2-12x+8ln|1+x|+4/(1+x)+C