Question

${\int }_0^{\infty }\frac{dt}{t^2+2t+2}$

Answer 1

$I={\int }_0^{\infty }\left(\frac{1}{(t+1{)}^2+1}\right)dt=\left[ta{n}^{-1}\right(t+1){]}_0^{\infty }=ta{n}^{-1}\infty -ta{n}^{-1}1=\pi /2-\pi /4=\pi /4$