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Homework Statement
1. Show that [tex]\int_0^\infty x^{n}e^{-ax}dx = \frac{n!} {a^{n+1}}[/tex]
for n = 0, 1, 2, 3...
2. Show that [tex]\int_{-\infty}^\infty x^{2n}e^{-ax^{2}}dx =\frac{{\surd \pi} (2n-1)!!} {2^{n}a^{(2n+1)/2}}[/tex]
for n = 0, 1, 2, 3...
Assumption: [tex]\int_{-\infty}^\infty e^{-ax^{2}}dx =\surd \frac{\pi} a [/tex]
a>0
3. Evaluate [tex]\int {\frac{1} {A^{x^2}+Bx+C}} dx [/tex]
For all possible real values of A, B, C.
For #1 and #2, you may use mathematical induction, if you like.
Notation: 7!! = 7 * 5 * 3 * 1
Homework Equations
The Attempt at a Solution
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