Integrate it in step by step applying integration by partial fraction.
∫(x^3)/(x^2+1)dx
First, do a long division
x^3/(x^2+1) = x - x/(x^2+1)
for the 2nd term, let u=x^2+1
∫(x^3)/(x^2+1)dx
x^3/(x^2+1) = x - x/(x^2+1)
for the 2nd term, let u=x^2+1