I was trying to compute the following integral but got stuck at the starting point. Can anyone provide a valuable hint for the evaluation of this integral $\int_{0}^{\infty}x^{9}e^{-x^{2}} dx$ ?
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2Integration by parts isn't helping? Here's a hint: Say that $u=x^2 \to \frac{1}{2}du=x dx$. – HDE 226868 Dec 13 '14 at 17:58
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Hint
Let $t=x^2$ and use the Gamma function.
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why is the Gamma function helpful? the result is a polynomial multiplied by the exponential function – Dr. Sonnhard Graubner Dec 13 '14 at 18:25
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for the indefinite integral $\int x^9e^{-x^2}dx$ the ansatz $$e^{-x^2}(Ax^8+Bx^6+Cx^4+Dx^2+E)$$ and compute the coeficients by differentiation with respect to $x$
Dr. Sonnhard Graubner
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