[tex]\displaystyle \mathtt{\int\limits \frac{x^3+x^2+x+1}{x^2+1}dx }\\ \\ \mathtt{x^3+x^2+x+1=x^2(x+1)+(x+1)=(x+1)(x^2+1)}\\ \\ \mathtt{\int\limits \frac{x^3+x^2+x+1}{x^2+1}dx =\int\limits \frac{(x+1)(x^2+1)}{x^2+1}dx=\int\limits (x+1)dx=}\\ \\ \mathtt{=\int\limits xdx+\int\limits1dx= \frac{x^2}{2} +x+C}[/tex]
