Optimal. Leaf size=20 \[ -1+8 \left (x+\frac {1}{5} \left (x+\frac {x}{\log (4)}\right )\right )+\log (x) \]
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Rubi [A] time = 0.01, antiderivative size = 18, normalized size of antiderivative = 0.90, number of steps used = 4, number of rules used = 3, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.130, Rules used = {12, 186, 43} \begin {gather*} \frac {8 x (1+6 \log (4))}{5 \log (4)}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 43
Rule 186
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {8 x+(5+48 x) \log (4)}{x} \, dx}{5 \log (4)}\\ &=\frac {\int \frac {5 \log (4)+8 x (1+6 \log (4))}{x} \, dx}{5 \log (4)}\\ &=\frac {\int \left (\frac {5 \log (4)}{x}+8 (1+6 \log (4))\right ) \, dx}{5 \log (4)}\\ &=\frac {8 x (1+6 \log (4))}{5 \log (4)}+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 14, normalized size = 0.70 \begin {gather*} \frac {8}{5} x \left (6+\frac {1}{\log (4)}\right )+\log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 21, normalized size = 1.05 \begin {gather*} \frac {48 \, x \log \relax (2) + 5 \, \log \relax (2) \log \relax (x) + 4 \, x}{5 \, \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 22, normalized size = 1.10 \begin {gather*} \frac {48 \, x \log \relax (2) + 5 \, \log \relax (2) \log \left ({\left | x \right |}\right ) + 4 \, x}{5 \, \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 14, normalized size = 0.70
method | result | size |
risch | \(\frac {48 x}{5}+\frac {4 x}{5 \ln \relax (2)}+\ln \relax (x )\) | \(14\) |
norman | \(\frac {4 \left (12 \ln \relax (2)+1\right ) x}{5 \ln \relax (2)}+\ln \relax (x )\) | \(17\) |
default | \(\frac {48 x \ln \relax (2)+4 x +5 \ln \relax (2) \ln \relax (x )}{5 \ln \relax (2)}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.81, size = 22, normalized size = 1.10 \begin {gather*} \frac {4 \, x {\left (12 \, \log \relax (2) + 1\right )} + 5 \, \log \relax (2) \log \relax (x)}{5 \, \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 16, normalized size = 0.80 \begin {gather*} \ln \relax (x)+\frac {x\,\left (48\,\ln \relax (2)+4\right )}{5\,\ln \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 20, normalized size = 1.00 \begin {gather*} \frac {x \left (4 + 48 \log {\relax (2 )}\right ) + 5 \log {\relax (2 )} \log {\relax (x )}}{5 \log {\relax (2 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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