I'm sorry, I've really tried to use MathJaX but I can't get integrals to work properly.

indefinite integral

$$\int {x\over x^4 +x^2 +1}$$

I set it up to equal

$$x\int {x\over x^4 +x^2 +1} - \int {x\over x^4 +x^2 +1}$$

$$\text{so } (x-1)\int {1\over x^4 +x^2 +1}$$

OKAY, now I set the denominator to $(X^2 +.5)^2 + \frac 34$

So I multiplied the top and bottom by $\frac 43$

then I absorbed it into the squared quantity by dividing it (within the parenthesis) by $\sqrt 3\over 2$

so

$${1\over \left({X^2 +.5\over {\sqrt 3\over 2}}\right)^2 + 1}$$

so $\arctan\left({X^2 +.5\over{\sqrt 3\over 2}}\right)$

FINAL ANSWER: $(x-1)\arctan\left({X^2 +.5\over{\sqrt 3\over 2}}\right) + C$

Thanks for reading, I have no way of checking this work... tutors are always have too many people wanting help.