I'm trying to solve to following integral (related to a previous post) $\int_{-1}^{1}\exp{(Ax^2+Bx+C+(Dx+E)\sqrt{1-x^2})}dx$ Any ideas on how to approach this?
Solving an integral with square root in the exponent
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integration
1 Answers
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There is no known closed-formula for the reduced case $B=C=D=E=0$ so I highly doubt you can find any magic answer. If you are lucky enough you will potentially end up using special functions like incomplete Gamma, which is not very easy to use.
If you are comfortable with approaching this integral numerically, I suggest using adaptive Gaussian quadrature with a sufficient number of roots.
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0Ok, thanks for your comments. It seems I'll have to tackle my [original question](http://math.stackexchange.com/questions/195210/integrate-a-3d-gaussian-over-a-sphere?lq=1) differently. – 2012-09-17