# Integration by Parts of <C> i just cannot do

1. Jun 4, 2005

### Rachael_Victoria

Can anyone outline, and this is a rather large request, the step by step integration by parts for <C>? This is not a homework question but more something i need to be able to do on tuesday for my final, and have been trying to do for two days.

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2. Jun 4, 2005

### dextercioby

Here's how it's done.

Knowing this integral's value

$$I'_{1}(\alpha)=:\int_{0}^{+\infty} C e^{-\alpha C^{2}} \ dC =\frac{1}{2\alpha}$$ (1)

,one sees immediately that

$$I'_{3}(\alpha)=:\int_{0}^{+\infty} C^{3} e^{-\alpha C^{2}} \ dC=-\frac{d}{d\alpha}I'_{1}=\frac{1}{2\alpha^{2}}$$ (2)

and now plug in (2) the expression for '\alpha'.

Daniel.

3. Jun 4, 2005

### Rachael_Victoria

Thank you, and you're right, i forgot to type the pi in the denominator for the answer.