I'm curious about the general solution to(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\int_{-\infty}^{+\infty} \exp[P(x)] dx [/itex]

Where P(x) is a polynomial in x with real coefficients and whose leading (highest) order is even and its leading order coefficient is negative. Intuitively these integrals ought to converge, but I'm having trouble calculating them.

I've been able to work out solutions for quadratics i.e. P(x) = -ax^2 +bx +c, but I'm thoroughly stuck w.r.t. quartic equations.

Has anyone ever seen anything like this? Gradshteyn & Rizhyk and mathematica have been of no use to me.

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# Integrals of Exponential(Polynomial(x)) dx Form

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