(A) We have,$I = \int \frac{x^4+x^2+1}{x^2-x+1} dx$. Since $x^4+x^2+1 = (x^2+1)^2 - x^2 = (x^2+x+1)(x^2-x+1)$,we can simplify the integrand: $I = \int

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$\frac{1}{3} x^3 + \frac{1}{2} x^2 + x + c$

(A) We have,$I = \int \frac{x^4+x^2+1}{x^2-x+1} dx$. Since $x^4+x^2+1 = (x^2+1)^2 - x^2 = (x^2+x+1)(x^2-x+1)$,we can simplify the integrand: $I = \int \frac{(x^2+x+1)(x^2-x+1)}{x^2-x+1} dx = \int (x^2+x+1) dx$. Integrating term by term,we get: $I = \frac{x^3}{3} + \frac{x^2}{2} + x + c$.