∫ x³/(x²+1) dx=∫ (x³+x-x)/(x²+1) dx=∫ xdx - ∫ x/(x²+1) dx=(1/2)x² - (1/2)∫ 1/(x²+1) d(x²)=(1/2)x² - (1/2)ln(x²+1) + C