find-dt-t-2-2t-2-

Question Number 28881 by abdo imad last updated on 31/Jan/18

f i n d \int_{- \infty}^{+ \infty} \frac{d t}{t^{2} + 2 t + 2}

Answered by sma3l2996 last updated on 01/Feb/18

I = \int_{- \infty}^{+ \infty} \frac{d t}{t^{2} + 2 t + 2} = \int_{- \infty}^{+ \infty} \frac{d t}{{(t + 1)}^{2} + 1}

u = t + 1 \Rightarrow d u = d t

I = \int_{- \infty}^{+ \infty} \frac{d u}{u^{2} + 1} = {[{t a n}^{- 1} (u)]}_{- \infty}^{+ \infty} = \frac{π}{2} - (- \frac{π}{2}) = π