Optimal. Leaf size=13 \[ 1+\frac {16 x^8}{\log (24)}+\log (x) \]
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Rubi [A] time = 0.01, antiderivative size = 12, normalized size of antiderivative = 0.92, number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 14} \begin {gather*} \frac {16 x^8}{\log (24)}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {128 x^8+\log (24)}{x} \, dx}{\log (24)}\\ &=\frac {\int \left (128 x^7+\frac {\log (24)}{x}\right ) \, dx}{\log (24)}\\ &=\frac {16 x^8}{\log (24)}+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 0.92 \begin {gather*} \frac {16 x^8}{\log (24)}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.07, size = 16, normalized size = 1.23 \begin {gather*} \frac {16 \, x^{8} + \log \left (24\right ) \log \relax (x)}{\log \left (24\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 19, normalized size = 1.46 \begin {gather*} \frac {128 \, x^{8} + \log \left (24\right ) \log \left (x^{8}\right )}{8 \, \log \left (24\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 13, normalized size = 1.00
method | result | size |
norman | \(\frac {16 x^{8}}{\ln \left (24\right )}+\ln \relax (x )\) | \(13\) |
default | \(\frac {16 x^{8}+\ln \left (24\right ) \ln \relax (x )}{\ln \left (24\right )}\) | \(17\) |
risch | \(\frac {16 x^{8}}{3 \ln \relax (2)+\ln \relax (3)}+\ln \relax (x )\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 19, normalized size = 1.46 \begin {gather*} \frac {128 \, x^{8} + \log \left (24\right ) \log \left (x^{8}\right )}{8 \, \log \left (24\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 12, normalized size = 0.92 \begin {gather*} \ln \relax (x)+\frac {16\,x^8}{\ln \left (24\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 14, normalized size = 1.08 \begin {gather*} \frac {16 x^{8} + \log {\left (24 \right )} \log {\relax (x )}}{\log {\left (24 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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