(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

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!

# Homework Help: 3 Challenging Integration problems

**Physics Forums | Science Articles, Homework Help, Discussion**