Optimal. Leaf size=26 \[ \log \left (\frac {2}{x \left (1+x+(10+x) \left (x+x^2\right )+\frac {\log (2)}{x}\right )}\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 20, normalized size of antiderivative = 0.77, number of steps
used = 1, number of rules used = 1, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {1601}
\begin {gather*} -\log \left (x^4+11 x^3+11 x^2+x+\log (2)\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 1601
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\log \left (x+11 x^2+11 x^3+x^4+\log (2)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 20, normalized size = 0.77 \begin {gather*} -\log \left (x+11 x^2+11 x^3+x^4+\log (2)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 21, normalized size = 0.81
method | result | size |
default | \(-\ln \left (\ln \left (2\right )+x^{4}+11 x^{3}+11 x^{2}+x \right )\) | \(21\) |
norman | \(-\ln \left (\ln \left (2\right )+x^{4}+11 x^{3}+11 x^{2}+x \right )\) | \(21\) |
risch | \(-\ln \left (\ln \left (2\right )+x^{4}+11 x^{3}+11 x^{2}+x \right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 20, normalized size = 0.77 \begin {gather*} -\log \left (x^{4} + 11 \, x^{3} + 11 \, x^{2} + x + \log \left (2\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 20, normalized size = 0.77 \begin {gather*} -\log \left (x^{4} + 11 \, x^{3} + 11 \, x^{2} + x + \log \left (2\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.18, size = 20, normalized size = 0.77 \begin {gather*} - \log {\left (x^{4} + 11 x^{3} + 11 x^{2} + x + \log {\left (2 \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 21, normalized size = 0.81 \begin {gather*} -\log \left ({\left | x^{4} + 11 \, x^{3} + 11 \, x^{2} + x + \log \left (2\right ) \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.07, size = 20, normalized size = 0.77 \begin {gather*} -\ln \left (x^4+11\,x^3+11\,x^2+x+\ln \left (2\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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