Optimal. Leaf size=13 \[ 81+\frac {1}{4} x \log (9 x \log (4)) \]
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Rubi [A] time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.85, number of steps used = 3, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 2295} \begin {gather*} \frac {1}{4} x \log (9 x \log (4)) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2295
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int (1+\log (9 x \log (4))) \, dx\\ &=\frac {x}{4}+\frac {1}{4} \int \log (9 x \log (4)) \, dx\\ &=\frac {1}{4} x \log (9 x \log (4))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 0.85 \begin {gather*} \frac {1}{4} x \log (9 x \log (4)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{4} \, x \log \left (18 \, x \log \relax (2)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.12, size = 26, normalized size = 2.00 \begin {gather*} \frac {1}{4} \, x + \frac {x \log \relax (2) \log \left (18 \, x \log \relax (2)\right ) - x \log \relax (2)}{4 \, \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 10, normalized size = 0.77
method | result | size |
derivativedivides | \(\frac {\ln \left (18 x \ln \relax (2)\right ) x}{4}\) | \(10\) |
default | \(\frac {\ln \left (18 x \ln \relax (2)\right ) x}{4}\) | \(10\) |
norman | \(\frac {\ln \left (18 x \ln \relax (2)\right ) x}{4}\) | \(10\) |
risch | \(\frac {\ln \left (18 x \ln \relax (2)\right ) x}{4}\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.37, size = 26, normalized size = 2.00 \begin {gather*} \frac {1}{4} \, x + \frac {x \log \relax (2) \log \left (18 \, x \log \relax (2)\right ) - x \log \relax (2)}{4 \, \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.41, size = 11, normalized size = 0.85 \begin {gather*} \frac {x\,\left (\ln \left (18\right )+\ln \left (\ln \relax (2)\right )+\ln \relax (x)\right )}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 10, normalized size = 0.77 \begin {gather*} \frac {x \log {\left (18 x \log {\relax (2 )} \right )}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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