What is the Integral of 1/(x^4+1) from 0 to b?

[dejet]

Homework Statement

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

Homework Equations

like i said i don't know where to go with this one.
i mean i know I am going to have to do integrate from 0 to b but i don't know where to start here.

The Attempt at a Solution

 

[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)

 

[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 can't be. thanks again. ill post with what i get to see if I am right.

 

[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.

 

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