Optimal. Leaf size=23 \[ \log \left (-x+\frac {1}{4} e^4 x^3 (4+x)+3 \log (\log (4))\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 24, normalized size of antiderivative = 1.04, number of steps used = 1, number of rules used = 1, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {1587} \begin {gather*} \log \left (-e^4 \left (x^4+4 x^3\right )+4 x-12 \log (\log (4))\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 1587
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (4 x-e^4 \left (4 x^3+x^4\right )-12 \log (\log (4))\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 25, normalized size = 1.09 \begin {gather*} \log \left (-4 x+4 e^4 x^3+e^4 x^4+12 \log (\log (4))\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 24, normalized size = 1.04 \begin {gather*} \log \left ({\left (x^{4} + 4 \, x^{3}\right )} e^{4} - 4 \, x + 12 \, \log \left (2 \, \log \relax (2)\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 25, normalized size = 1.09 \begin {gather*} \log \left ({\left | {\left (x^{4} + 4 \, x^{3}\right )} e^{4} - 4 \, x + 12 \, \log \left (2 \, \log \relax (2)\right ) \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 27, normalized size = 1.17
method | result | size |
derivativedivides | \(\ln \left (12 \ln \left (2 \ln \relax (2)\right )+\left (x^{4}+4 x^{3}\right ) {\mathrm e}^{4}-4 x \right )\) | \(27\) |
risch | \(\ln \left (x^{4} {\mathrm e}^{4}+4 x^{3} {\mathrm e}^{4}+12 \ln \relax (2)+12 \ln \left (\ln \relax (2)\right )-4 x \right )\) | \(28\) |
default | \(\ln \left (x^{4} {\mathrm e}^{4}+4 x^{3} {\mathrm e}^{4}+12 \ln \left (2 \ln \relax (2)\right )-4 x \right )\) | \(30\) |
norman | \(\ln \left (x^{4} {\mathrm e}^{4}+4 x^{3} {\mathrm e}^{4}+12 \ln \left (2 \ln \relax (2)\right )-4 x \right )\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 25, normalized size = 1.09 \begin {gather*} \log \left (x^{4} e^{4} + 4 \, x^{3} e^{4} - 4 \, x + 12 \, \log \left (2 \, \log \relax (2)\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.22, size = 23, normalized size = 1.00 \begin {gather*} \ln \left ({\mathrm {e}}^4\,x^4+4\,{\mathrm {e}}^4\,x^3-4\,x+\ln \left ({\ln \relax (4)}^{12}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.64, size = 31, normalized size = 1.35 \begin {gather*} \log {\left (x^{4} e^{4} + 4 x^{3} e^{4} - 4 x + 12 \log {\left (\log {\relax (2 )} \right )} + 12 \log {\relax (2 )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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