calculate-2-e-x-x-2-dx-

Question Number 65665 by mathmax by abdo last updated on 01/Aug/19

c a l c u l a t e \int_{- 2}^{+ \infty} \frac{e^{- x}}{\sqrt{x + 2}} d x

Commented by mathmax by abdo last updated on 02/Aug/19

l e t I = \int_{- 2}^{+ \infty} \frac{e^{- x}}{\sqrt{x + 2}} d x c h a n g e m e n t \sqrt{x + 2} = t g i v e x + 2 = t^{2} \Rightarrow

I = \int_{0}^{+ \infty} \frac{e^{- (t^{2} - 2)}}{t} (2 t) d t = 2 \int_{0}^{+ \infty} e^{- t^{2} + 2} d t = e^{2} \int_{- \infty}^{+ \infty} e^{- t^{2}} d t

= e^{2} \sqrt{π}