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∫(x^2-1)/(x^4+x^2+1)dx
=∫ [ (x-0.5)/(x²-x+1) - (x+0.5)/(x²+x+1) ]dx
设y=x-0.5 z=x+0.5
∫ [ (x-0.5)/(x²-x+1) - (x+0.5)/(x²+x+1) ]dx
=∫ ydy/(y²+0.75) + ∫ zdz/(z²+0.75)
=0.5*ln(y²+0.75) + 0.5*ln(z²+0.75) + C
=0.5*ln(x²-x+1) + 0.5*ln(x²+x+1) + C
=∫ [ (x-0.5)/(x²-x+1) - (x+0.5)/(x²+x+1) ]dx
设y=x-0.5 z=x+0.5
∫ [ (x-0.5)/(x²-x+1) - (x+0.5)/(x²+x+1) ]dx
=∫ ydy/(y²+0.75) + ∫ zdz/(z²+0.75)
=0.5*ln(y²+0.75) + 0.5*ln(z²+0.75) + C
=0.5*ln(x²-x+1) + 0.5*ln(x²+x+1) + C
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