Question

求不定积分,∫x^4/x+1dx

Answer 1

∫(x^4-1+1)/(x+1)dx
=∫(x^2-1)(x^2+1)/(x+1)dx+∫1/(x+1)dx
=∫(x-1)(x^2+1)dx+∫1/(x+1)dx
=∫(x^3-x^2+x-1)dx+∫1/(x+1)dx
=x^4/4-x^3/3+x^2/2-x+ln|x+1|+C