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I need to evaluate the following integral

$$ \int_{-\infty}^\infty e^{-2x^2+7x} dx$$

I've tried u substitution, integration by parts, and splitting apart the exponent and don't seem to be making any progress.

Thanks for your help

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    This integral cannot be explicited in terms of elementary functions ... except if you consider $erf$ beeing an elementary function. – 2017-01-23
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    @kelly do you want it in specific interval.? – 2017-01-23
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    @MyGlasses It says from $-\infty$ to $\infty$. – 2017-01-23
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    I didn't hear kelly say that – 2017-01-23
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    Note that the integrand in the title differs from the integrand in the body of the question. Which is correct? – 2017-01-23

1 Answers 1

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Note that $$\int_{-\infty}^{\infty} e^{-2x^2 + 7x}dx=\int_{-\infty}^{\infty} e^{-2(x-7/4)^2}e^{49/8}dx$$ Then let $u=\sqrt{2}(x-\frac{7}{4})$ and recall $$ \int_{-\infty}^{\infty} e^{-u^{2}}du=\sqrt{\pi}.$$

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    Yourself take an interval and sole it.? – 2017-01-23
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    @MyGlasses He didn't write the limits in the integral, but it explicitly said (before the edit) "I need to evaluate the following integral from -infinty to infinity" – 2017-01-23
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    I don't see anything. – 2017-01-23
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    You can check the edit history. – 2017-01-23
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    @myglasses I didn't read the pre-edited version, but I've read the history log and the reference was there. The user who edited deleted it and ought to be admonished to refrain from editing content that augments questions. – 2017-01-23