How to integrate: $\int_0^{\infty} \frac{1}{x^3+x^2+x+1}dx$ I want to evaluate $\int_0^{\infty} \frac{1}{x^3+x^2+x+1}$. The lecture only provided me with a formula for $\int_{-\infty}^{\infty}dx \frac{A}{B}$ where $A,B$ are polynomials and $B$ does not have real zeros. Unfortunately, in the given case $B$ has a zero at $z=-1$ and is not even. Is there a straight forward way to solve this in terms of complex analysis?

$$\frac{1}{x^3+x^2+x+1}=\frac{1}{(x+1)(x^2+1)}=\frac{1}{2}\left(\frac{1}{1+x}-\frac{x}{x^2+1}+\frac{1}{x^2+1}\right)$$
