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optimal antiderivative for 1/((x^2+x+1)*SQRT(x^2-x+1))
Posted:
Oct 15, 2011 4:09 AM
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Derive 6.10 returns these elementary integrals unevaluated:
INT(1/((x^2 + x + 1)*SQRT(x^2 - x + 1)), x)
INT(x/((x^2 + x + 1)*SQRT(x^2 - x + 1)), x)
The optimal antiderivatives are:
ATANH(SQRT(6)*(x - 1)/(3*SQRT(x^2 - x + 1)))/SQRT(6)
+ ATAN(SQRT(2)*(x + 1)/SQRT(x^2 - x + 1))/SQRT(2)
ATANH(SQRT(6)*(x - 1)/(3*SQRT(x^2 - x + 1)))/SQRT(6)
- ATAN(SQRT(2)*(x + 1)/SQRT(x^2 - x + 1))/SQRT(2)
Is there an integrator clever enough to find them?
Martin.
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