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