# Integral of 1/(1+x^4) dx

1. Mar 21, 2013

### vokurka

∫1/(1+x^4) dx, from 0 to ∞

I have tried integration per partes, several different substitutions and transformation into different coordinate system but i have always only found another equivalent integral that i was not able to solve... I have also performed a numerical integration, but i need an analytical solution...
Thanks

2. Mar 21, 2013

### SteamKing

Staff Emeritus
You should be able to work out the indefinite integral with one substitution. By the way, what is the derivative of the arc tangent?

3. Mar 21, 2013

### Ray Vickson

Partial fractions.

4. Mar 22, 2013

### Curious3141

Hint: $x^4 + 1 = (x^2+1)^2 - (\sqrt{2}x)^2$. Rearrange, factorise.

Then use what Ray suggested.

5. Mar 23, 2013

### SithsNGiggles

Try substituting $\sqrt{u}=x$.

Edit: Sorry, this doesn't actually work. Disregard!

Last edited: Mar 23, 2013
6. Mar 23, 2013

### Dick

You have a definite integral. I'd suggest using contour integration and the residue theorem if you know that technique.