∫(x^3+1)/(1+x^2)dx=∫(x^3+x-x+1)/(1+x^2)dx=∫xdx + ∫(-x)/(1+x^2)dx + ∫1/(1+x^2)dx=(1/2)x² - (1/2)ln(1+x²) + arctan(x) +C