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.

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

Loading...

Similar Threads for Integrals Exponential Polynomial | Date |
---|---|

I Decomposing a Certain Exponential Integral | Apr 12, 2018 |

A Closed form for series over Exponential Integral | Feb 16, 2017 |

I Integral of third order polynomial exponential | May 7, 2016 |

Integral of Exponential with Polynomial Argument | Jul 4, 2015 |

Integral of an exponential that has a polynomial | Apr 29, 2012 |

**Physics Forums - The Fusion of Science and Community**