find-e-x-2-2x-1-dx-

Question Number 31104 by abdo imad last updated on 02/Mar/18

f i n d \int_{- \infty}^{+ \infty} e^{- (x^{2} + 2 x - 1)} d x .

Commented by abdo imad last updated on 03/Mar/18

I = \int_{- \infty}^{+ \infty} e^{- ({(x + 1)}^{2} - 2)} d x = e^{2} \int_{- \infty}^{+ \infty} e^{- {(x + 1)}^{2}} d x a n d t h e

c h . x + 1 = u g i v e I = e^{2} \int_{- \infty}^{+ \infty} e^{- u^{2}} d u \Rightarrow I = \sqrt{π} e^{2} .