Optimal. Leaf size=19 \[ 1-\log \left (6+e^5-x^2-2 \log (4)\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 0.89, number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {12, 260} \begin {gather*} -\log \left (-x^2+e^5+6-2 \log (4)\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 260
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (2 \int \frac {x}{-6-e^5+x^2+2 \log (4)} \, dx\right )\\ &=-\log \left (6+e^5-x^2-2 \log (4)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 0.89 \begin {gather*} -\log \left (6+e^5-x^2-2 \log (4)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 16, normalized size = 0.84 \begin {gather*} -\log \left (x^{2} - e^{5} + 4 \, \log \relax (2) - 6\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 17, normalized size = 0.89 \begin {gather*} -\log \left ({\left | x^{2} - e^{5} + 4 \, \log \relax (2) - 6 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.25, size = 17, normalized size = 0.89
method | result | size |
derivativedivides | \(-\ln \left (4 \ln \relax (2)-{\mathrm e}^{5}+x^{2}-6\right )\) | \(17\) |
default | \(-\ln \left (6-x^{2}-4 \ln \relax (2)+{\mathrm e}^{5}\right )\) | \(17\) |
norman | \(-\ln \left (6-x^{2}-4 \ln \relax (2)+{\mathrm e}^{5}\right )\) | \(17\) |
risch | \(-\ln \left (4 \ln \relax (2)-{\mathrm e}^{5}+x^{2}-6\right )\) | \(17\) |
meijerg | \(\frac {\left ({\mathrm e}^{5}-4 \ln \relax (2)+6\right ) \ln \left (1-\frac {x^{2}}{{\mathrm e}^{5}-4 \ln \relax (2)+6}\right )}{-{\mathrm e}^{5}+4 \ln \relax (2)-6}\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 16, normalized size = 0.84 \begin {gather*} -\log \left (x^{2} - e^{5} + 4 \, \log \relax (2) - 6\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.18, size = 14, normalized size = 0.74 \begin {gather*} -\ln \left (x^2-{\mathrm {e}}^5+\ln \left (16\right )-6\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 15, normalized size = 0.79 \begin {gather*} - \log {\left (x^{2} - e^{5} - 6 + 4 \log {\relax (2 )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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