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divide both numerator and denom by x^2 to get(3x^2 – 1/x^2)/(1+1/x+x^3)^2now put 1+1/x+x^3=yso that dy/dx= 3x^2 – 1/x^2so, the integral becomes 1/y^2we get – 1/y= – 1/(1+1/x+x^3) + C= –x/(x^4+x+1)+C
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