Optimal. Leaf size=15 \[ -\log \left (-1+e^{-2+x-x^6}\right ) \]
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Rubi [A] time = 0.12, antiderivative size = 27, normalized size of antiderivative = 1.80, number of steps used = 1, number of rules used = 1, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {6684} \begin {gather*} -\log \left (-e^{-x^6-2} \left (e^x-e^{x^6+2}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\log \left (-e^{-2-x^6} \left (e^x-e^{2+x^6}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.10, size = 20, normalized size = 1.33 \begin {gather*} x^6-\log \left (e^x-e^{2+x^6}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.78, size = 14, normalized size = 0.93 \begin {gather*} -\log \left (e^{\left (-x^{6} + x - 2\right )} - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.44, size = 16, normalized size = 1.07 \begin {gather*} -\log \left (-e^{\left (-x^{6} + x - 2\right )} + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 15, normalized size = 1.00
method | result | size |
norman | \(-\ln \left ({\mathrm e}^{-x^{6}+x -2}-1\right )\) | \(15\) |
risch | \(-2-\ln \left ({\mathrm e}^{-x^{6}+x -2}-1\right )\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 21, normalized size = 1.40 \begin {gather*} x^{6} - \log \left ({\left (e^{\left (x^{6} + 2\right )} - e^{x}\right )} e^{\left (-2\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.12, size = 14, normalized size = 0.93 \begin {gather*} -\ln \left ({\mathrm {e}}^{-x^6+x-2}-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 12, normalized size = 0.80 \begin {gather*} - \log {\left (e^{- x^{6} + x - 2} - 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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