Optimal. Leaf size=24 \[ \log \left (4-x+16 \left (x-\frac {-x+\log (x)}{24 \log (4)}\right )\right ) \]
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Rubi [F] time = 0.21, 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 {2-2 x-45 x \log (4)}{-2 x^2+\left (-12 x-45 x^2\right ) \log (4)+2 x \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 {2+x (-2-45 \log (4))}{-2 x^2+\left (-12 x-45 x^2\right ) \log (4)+2 x \log (x)} \, dx\\ &=\int \left (\frac {2+45 \log (4)}{12 \log (4)+2 x \left (1+\frac {45 \log (4)}{2}\right )-2 \log (x)}+\frac {2}{x \left (-12 \log (4)-2 x \left (1+\frac {45 \log (4)}{2}\right )+2 \log (x)\right )}\right ) \, dx\\ &=2 \int \frac {1}{x \left (-12 \log (4)-2 x \left (1+\frac {45 \log (4)}{2}\right )+2 \log (x)\right )} \, dx+(2+45 \log (4)) \int \frac {1}{12 \log (4)+2 x \left (1+\frac {45 \log (4)}{2}\right )-2 \log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.12, size = 18, normalized size = 0.75 \begin {gather*} \log (2 x+12 \log (4)+45 x \log (4)-2 \log (x)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 16, normalized size = 0.67 \begin {gather*} \log \left (-3 \, {\left (15 \, x + 4\right )} \log \relax (2) - x + \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 16, normalized size = 0.67 \begin {gather*} \log \left (-45 \, x \log \relax (2) - x - 12 \, \log \relax (2) + \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 17, normalized size = 0.71
method | result | size |
norman | \(\ln \left (45 x \ln \relax (2)+12 \ln \relax (2)+x -\ln \relax (x )\right )\) | \(17\) |
risch | \(\ln \left (-45 x \ln \relax (2)+\ln \relax (x )-12 \ln \relax (2)-x \right )\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 17, normalized size = 0.71 \begin {gather*} \log \left (-x {\left (45 \, \log \relax (2) + 1\right )} - 12 \, \log \relax (2) + \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.73, size = 16, normalized size = 0.67 \begin {gather*} \ln \left (x+12\,\ln \relax (2)-\ln \relax (x)+45\,x\,\ln \relax (2)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 17, normalized size = 0.71 \begin {gather*} \log {\left (- 45 x \log {\relax (2 )} - x + \log {\relax (x )} - 12 \log {\relax (2 )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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