# Integrate from 0 to b

1. Jun 23, 2008

### dejet

1. The problem statement, all variables and given/known data
i do not know where to start with this one can anyone point me where to go please?

$$\int \frac{1}{x^{4}+1}$$

lower limit = 0 upper = infinity

2. Relevant equations

like i said i dont know where to go with this one.
i mean i know im going to have to do integrate from 0 to b but i dont know where to start here.
3. The attempt at a solution

2. Jun 23, 2008

### rootX

It seems really messy if you integrate using substitutions ... etc.

I would recommend using f = 1/(x^2.y^2+1)

some matlab mess

>> f = 1/(x^4+1)

f =

1/(x^4+1)

>> int(f,x,0,inf)

ans =

1/4*pi*2^(1/2)

>> int(f,x)

ans =

1/8*2^(1/2)*log((x^2+x*2^(1/2)+1)/(x^2-x*2^(1/2)+1))+1/4*2^(1/2)*atan(x*2^(1/2)+1)+1/4*2^(1/2)*atan(x*2^(1/2)-1)

3. Jun 23, 2008

### dejet

o wait i think i need to compare i think i have it ill repost. thanks rootX seeing your answer made me see that we have yet to really learn that, so it cant be. thanks again. ill post with what i get to see if im right.

4. Jun 23, 2008

### Defennder

Here some hints to get you going. You'll have to decompose it to partial fractions, complete a square, and then use the derivative for arctan f(x). It's quite tedious, but most certainly doable.

5. Jun 24, 2008

### m_s_a

Re: integrate

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cont.
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Last edited by a moderator: May 3, 2017