int x^3/(x^4+1)dx + int x/(x^4+1)dx = int d(x^4/3)/(x^4+1) + int d(x^2/2)/(x^4+1) = 1/4 int d(x^4+1)/(x^4+1) + 1/2 int d(x^2+1)/(x^4+1)..так вроде получается?
Тогда 1/4*ln|x^4+1| + 1/2*arctg(x^2) + C..?