Optimal. Leaf size=19 \[ 6 x-\log (4) \log \left (\frac {5}{x}-\log (x)\right ) \]
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Rubi [F]
time = 0.31, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {-30 x+(-5-x) \log (4)+6 x^2 \log (x)}{-5 x+x^2 \log (x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-30 x+(-5-x) \log (4)+6 x^2 \log (x)}{x^2 \left (-\frac {5}{x}+\log (x)\right )} \, dx\\ &=\int \frac {-30 x+(-5-x) \log (4)+6 x^2 \log (x)}{x (-5+x \log (x))} \, dx\\ &=\int \left (6-\frac {(5+x) \log (4)}{x (-5+x \log (x))}\right ) \, dx\\ &=6 x-\log (4) \int \frac {5+x}{x (-5+x \log (x))} \, dx\\ &=6 x-\log (4) \int \left (\frac {1}{-5+x \log (x)}+\frac {5}{x (-5+x \log (x))}\right ) \, dx\\ &=6 x-\log (4) \int \frac {1}{-5+x \log (x)} \, dx-(5 \log (4)) \int \frac {1}{x (-5+x \log (x))} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 21, normalized size = 1.11 \begin {gather*} 6 x+\log (4) \log (x)-\log (4) \log (5-x \log (x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.23, size = 22, normalized size = 1.16
method | result | size |
risch | \(6 x -2 \ln \left (2\right ) \ln \left (\ln \left (x \right )-\frac {5}{x}\right )\) | \(18\) |
default | \(6 x -2 \ln \left (2\right ) \ln \left (x \ln \left (x \right )-5\right )+2 \ln \left (2\right ) \ln \left (x \right )\) | \(22\) |
norman | \(6 x -2 \ln \left (2\right ) \ln \left (x \ln \left (x \right )-5\right )+2 \ln \left (2\right ) \ln \left (x \right )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.51, size = 19, normalized size = 1.00 \begin {gather*} -2 \, \log \left (2\right ) \log \left (\frac {x \log \left (x\right ) - 5}{x}\right ) + 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 19, normalized size = 1.00 \begin {gather*} -2 \, \log \left (2\right ) \log \left (\frac {x \log \left (x\right ) - 5}{x}\right ) + 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 15, normalized size = 0.79 \begin {gather*} 6 x - 2 \log {\left (2 \right )} \log {\left (\log {\left (x \right )} - \frac {5}{x} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 21, normalized size = 1.11 \begin {gather*} -2 \, \log \left (2\right ) \log \left (x \log \left (x\right ) - 5\right ) + 2 \, \log \left (2\right ) \log \left (x\right ) + 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.89, size = 21, normalized size = 1.11 \begin {gather*} 6\,x-2\,\ln \left (2\right )\,\ln \left (x\,\ln \left (x\right )-5\right )+2\,\ln \left (2\right )\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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