How to evaluate $\int^\infty_{-\infty} \frac{dx}{4x^2+4x+5}$? I need help in my calculus homework guys, I can't find a way to integrate this, I tried use partial fractions or u-substitutions but it didn't work.
$$\int^\infty_{-\infty} \frac{dx}{4x^2+4x+5}$$
Thanks much for the help!

Use Residue Theorem.
$$\int_{-\infty}^{\infty}\frac{dx}{4x^2+4x+5}=\int_C\frac{dz}{4z^2+4z+5}=2\pi i\text{Res}|_{z=-\frac{1}{2}+i}=2\pi i\frac{1}{2i}=\pi.$$
