∫x^4/(1+x)]dx
=∫[(x^4-1)+1]/(1+x)]dx
=∫(x^4-1)/(1+x)+∫1/(1+x)dx
=∫(x²+1)(x²-1)/(1+x)dx+∫1/(1+x)dx
=∫(x²+1)(x-1)dx+∫1/(1+x)dx
=∫(x^3-x²+x)dx-∫dx+∫1/(1+x)dx
=x^4/4-x³/3+x^2/2-x+ln(1+x)+C