What will be the integral of $\dfrac{x^3+x+1}{x^4+x^2+1}$? I tried dividing the denominator by the numerator but it didn't work. I also tried partial fractions but I seem to be doing something wrong.
2026-05-14 10:07:06.1778753226
Indefinite integration of rational functions
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First note that $x^4+x^2+1 = (x^4+2x^2+1) - x^2 = (x^2+1)^2-x^2 = (x^2+x+1)(x^2-x+1)$ So we have the following: $(x^3+x+1)/(x^4+x^2+1) = ((x+1)(x^2-x+1) + x)/((x^2+x+1)(x^2-x+1))$ The rest should be too simple, try it.