Is there an easy way to compute $$\int_{-\infty}^\infty\exp(-x^2+2x)\mathrm{d}x$$ without using a computer package?
How to evalutate this exponential integral
9
$\begingroup$
calculus
integration
definite-integrals
improper-integrals
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4Try completing the square in the exponent. – 2012-06-28
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1$\exp(-x^2+2x)=\exp(-(x-1)^2)/e$, and substituting with $u=x-1$. – 2012-06-28
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0Thank you both for your comments, I've just figured it out. – 2012-06-28
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0I judt ran into this. Found a solution in larsons problem solving through problems. Problem 1 ,4 ,4. He squares entire integral. https://www.google.com/url?sa=t&source=web&rct=j&url=https://math.la.asu.edu/~ifulman/spring13/mat194/problem-solving.pdf&ved=2ahUKEwjop5ueza_cAhUJjFQKHVjmDwcQFjAAegQIABAB&usg=AOvVaw3ojecQy5DfCOW9Us_cozGx – 2018-07-21