# Integral of 1/(x^6+1)

1. Sep 25, 2013

### freshman2013

1. The problem statement, all variables and given/known data

basically the title

2. Relevant equations

3. The attempt at a solution
so I tried writing it as a difference of squares and got (x^3+1+sqrt(2)*x^1.5)(x^3+1-sqrt(2)x^1.5)
and I attempted partial fractions and I don't know if I did anything wrong, but then I got stuck when it came time to solve for the variables in the partial fraction decomposition. I'm not lost on this problem so If anyone has any clue, please guide me in the right direction. Thanks!

2. Sep 25, 2013

### debsankar

I am not good at integrations... but here is a answer kind of thing done in mathematica....
you can check your results with it...

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3. Sep 25, 2013

Try writing $1 + x^6$ as a sum of two cubes:
$$1+x^6 = 1 + \left(x^2\right)^3$$

and factor, then apply partial fractions.

4. Sep 25, 2013

### juantheron

Hint :: $\displaystyle \int\frac{1}{1+x^6}dx = \frac{1}{2}\int\frac{(1+x^4)+(1-x^4)}{1+x^6}dx$

and Break into two parts $I$ and $J$