Optimal. Leaf size=17 \[ \log \left (5 x+\frac {x^2}{\log (4)}\right )+\log (\log (27)) \]
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Rubi [A]
time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.59, number of steps
used = 1, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {642}
\begin {gather*} \log \left (x^2+5 x \log (4)\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 642
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (x^2+5 x \log (4)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 10, normalized size = 0.59 \begin {gather*} \log (x)+\log (x+5 \log (4)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 10, normalized size = 0.59
method | result | size |
default | \(\ln \left (x \left (10 \ln \left (2\right )+x \right )\right )\) | \(10\) |
derivativedivides | \(\ln \left (10 x \ln \left (2\right )+x^{2}\right )\) | \(11\) |
norman | \(\ln \left (x \right )+\ln \left (10 \ln \left (2\right )+x \right )\) | \(11\) |
risch | \(\ln \left (10 x \ln \left (2\right )+x^{2}\right )\) | \(11\) |
meijerg | \(\ln \left (1+\frac {x}{10 \ln \left (2\right )}\right )+\ln \left (x \right )-\ln \left (2\right )-\ln \left (5\right )-\ln \left (\ln \left (2\right )\right )\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 10, normalized size = 0.59 \begin {gather*} \log \left (x^{2} + 10 \, 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 = 0.29, size = 10, normalized size = 0.59 \begin {gather*} \log \left (x^{2} + 10 \, 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 = 0.05, size = 10, normalized size = 0.59 \begin {gather*} \log {\left (x^{2} + 10 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 = 0.39, size = 15, normalized size = 0.88 \begin {gather*} \log \left (2 \, {\left | \frac {1}{2} \, x^{2} + 5 \, 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 = 0.08, size = 9, normalized size = 0.53 \begin {gather*} \ln \left (x\,\left (x+10\,\ln \left (2\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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