- #1

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## Homework Statement

[tex]\int^{\infty}_{-\infty}(1/(a^{4}+(x-x_{0})^{4}))dx[/tex]

## Homework Equations

## The Attempt at a Solution

i let [tex]u = (x-x_{0})^{4}[/tex]

but have no idea what to go from there

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- Thread starter z00maffect
- Start date

- #1

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[tex]\int^{\infty}_{-\infty}(1/(a^{4}+(x-x_{0})^{4}))dx[/tex]

i let [tex]u = (x-x_{0})^{4}[/tex]

but have no idea what to go from there

Last edited:

- #2

Dick

Science Advisor

Homework Helper

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- #3

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awesome thanks! got [tex]\pi*\sqrt{2}/2[/tex]

- #4

Dick

Science Advisor

Homework Helper

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awesome thanks! got [tex]\pi*\sqrt{2}/2[/tex]

Good job. Don't forget to put the 'a' factor back in again.

- #5

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u=\frac{x-x_{0}}{a} [/tex] then [tex] du= adx [/tex] and now integral becomes

[tex]

\frac{1}{a^{5}}\int^{\infty}_{-\infty}\frac{1}{1+u^{4}}du

[/tex]

Secondly, by letting [tex] u=e^{i\theta} [/tex] and [tex] du=i*{e}^{i\theta}d\theta[/tex]

you can use "residue theorem". Yet, I forgot how can we apply here. After I remember, I'll post it

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