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

$$find{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}{e}^{-(x^2+2x-1)}dx.$$

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

$$I={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}{e}^{-({(x+1)}^2-2)}dx=e^2{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}{e}^{-{(x+1)}^2}dxandthe$$$$ch.x+1=ugiveI=e^2{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}{e}^{-u^2}du\Rightarrow I=\sqrt{\pi }{e}^2.$$

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