- #1

jimmychim

- 3

- 0

## 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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