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!

*

*Manipulate the denominator to get $(2x+1)^2 + 4 = (2x+1)^2 + 2^2$. 

*Let $u = 2x+1 \implies du = 2 dx \implies dx = \frac 12 du$,

*$\displaystyle \frac 12 \int_{-\infty}^\infty \dfrac{du}{u^2 + (2)^2} $

*use an appropriate trig substitution which you should recognize: 
$$ \int\frac{du}{{u^2 + a^2}} = \frac{1}{a} \arctan \left(\frac{u}{a}\right)+C $$
