Optimal. Leaf size=18 \[ \log \left (\frac {1}{25} \left (2 x+\frac {x^4}{4}\right )^4\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 10, normalized size of antiderivative = 0.56, number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {1587} \begin {gather*} 4 \log \left (x^4+8 x\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 1587
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=4 \log \left (8 x+x^4\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 0.72 \begin {gather*} 4 \log (x)+4 \log \left (8+x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 10, normalized size = 0.56 \begin {gather*} 4 \, \log \left (x^{4} + 8 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 15, normalized size = 0.83 \begin {gather*} 4 \, \log \left (4 \, {\left | \frac {1}{4} \, x^{4} + 2 \, x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.33, size = 11, normalized size = 0.61
method | result | size |
default | \(4 \ln \left (x \left (x^{3}+8\right )\right )\) | \(11\) |
risch | \(4 \ln \left (x^{4}+8 x \right )\) | \(11\) |
meijerg | \(4 \ln \left (1+\frac {x^{3}}{8}\right )+4 \ln \relax (x )-4 \ln \relax (2)\) | \(20\) |
norman | \(4 \ln \relax (x )+4 \ln \left (2+x \right )+4 \ln \left (x^{2}-2 x +4\right )\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.66, size = 10, normalized size = 0.56 \begin {gather*} 4 \, \log \left (x^{4} + 8 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 10, normalized size = 0.56 \begin {gather*} 4\,\ln \left (x^4+8\,x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 8, normalized size = 0.44 \begin {gather*} 4 \log {\left (x^{4} + 8 x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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