Optimal. Leaf size=26 \[ 4 (-1+x) x \left (5+\frac {5}{x}-\frac {7-x}{\log (3)}\right ) \log (x) \]
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Rubi [A] time = 0.10, antiderivative size = 48, normalized size of antiderivative = 1.85, number of steps used = 10, number of rules used = 6, integrand size = 56, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.107, Rules used = {12, 14, 765, 2356, 2295, 2304} \begin {gather*} \frac {4 x^3 \log (x)}{\log (3)}-\frac {4 x^2 (8-\log (243)) \log (x)}{\log (3)}+\frac {28 x \log (x)}{\log (3)}-\frac {4 \log (243) \log (x)}{\log (3)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 765
Rule 2295
Rule 2304
Rule 2356
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {28 x-32 x^2+4 x^3+\left (-20+20 x^2\right ) \log (3)+\left (28 x-64 x^2+12 x^3+40 x^2 \log (3)\right ) \log (x)}{x} \, dx}{\log (3)}\\ &=\frac {\int \left (\frac {4 (1-x) \left (-x^2+x (7-\log (243))-\log (243)\right )}{x}+4 \left (7+3 x^2-2 x (8-\log (243))\right ) \log (x)\right ) \, dx}{\log (3)}\\ &=\frac {4 \int \frac {(1-x) \left (-x^2+x (7-\log (243))-\log (243)\right )}{x} \, dx}{\log (3)}+\frac {4 \int \left (7+3 x^2-2 x (8-\log (243))\right ) \log (x) \, dx}{\log (3)}\\ &=\frac {4 \int \left (7+x^2-x (8-\log (243))-\frac {\log (243)}{x}\right ) \, dx}{\log (3)}+\frac {4 \int \left (7 \log (x)+3 x^2 \log (x)+2 x (-8+\log (243)) \log (x)\right ) \, dx}{\log (3)}\\ &=\frac {28 x}{\log (3)}+\frac {4 x^3}{3 \log (3)}-\frac {2 x^2 (8-\log (243))}{\log (3)}-\frac {4 \log (243) \log (x)}{\log (3)}+\frac {12 \int x^2 \log (x) \, dx}{\log (3)}+\frac {28 \int \log (x) \, dx}{\log (3)}-\frac {(8 (8-\log (243))) \int x \log (x) \, dx}{\log (3)}\\ &=\frac {28 x \log (x)}{\log (3)}+\frac {4 x^3 \log (x)}{\log (3)}-\frac {4 x^2 (8-\log (243)) \log (x)}{\log (3)}-\frac {4 \log (243) \log (x)}{\log (3)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 39, normalized size = 1.50 \begin {gather*} \frac {4 \left (7 x \log (x)-8 x^2 \log (x)+x^3 \log (x)-\log (243) \log (x)+x^2 \log (243) \log (x)\right )}{\log (3)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 29, normalized size = 1.12 \begin {gather*} \frac {4 \, {\left (x^{3} - 8 \, x^{2} + 5 \, {\left (x^{2} - 1\right )} \log \relax (3) + 7 \, x\right )} \log \relax (x)}{\log \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 33, normalized size = 1.27 \begin {gather*} \frac {4 \, {\left ({\left (x^{3} + x^{2} {\left (5 \, \log \relax (3) - 8\right )} + 7 \, x\right )} \log \relax (x) - 5 \, \log \relax (3) \log \relax (x)\right )}}{\log \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 34, normalized size = 1.31
method | result | size |
risch | \(\frac {\left (20 x^{2} \ln \relax (3)+4 x^{3}-32 x^{2}+28 x \right ) \ln \relax (x )}{\ln \relax (3)}-20 \ln \relax (x )\) | \(34\) |
norman | \(-20 \ln \relax (x )+\frac {28 x \ln \relax (x )}{\ln \relax (3)}+\frac {4 x^{3} \ln \relax (x )}{\ln \relax (3)}+\frac {4 \left (5 \ln \relax (3)-8\right ) x^{2} \ln \relax (x )}{\ln \relax (3)}\) | \(43\) |
default | \(\frac {40 \ln \relax (3) \left (\frac {x^{2} \ln \relax (x )}{2}-\frac {x^{2}}{4}\right )+4 x^{3} \ln \relax (x )-32 x^{2} \ln \relax (x )+10 x^{2} \ln \relax (3)+28 x \ln \relax (x )-20 \ln \relax (3) \ln \relax (x )}{\ln \relax (3)}\) | \(56\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.39, size = 56, normalized size = 2.15 \begin {gather*} \frac {2 \, {\left (2 \, x^{3} \log \relax (x) + 5 \, x^{2} \log \relax (3) - 16 \, x^{2} \log \relax (x) + 5 \, {\left (2 \, x^{2} \log \relax (x) - x^{2}\right )} \log \relax (3) + 14 \, x \log \relax (x) - 10 \, \log \relax (3) \log \relax (x)\right )}}{\log \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.56, size = 41, normalized size = 1.58 \begin {gather*} \frac {28\,x\,\ln \relax (x)}{\ln \relax (3)}-20\,\ln \relax (x)+\frac {4\,x^3\,\ln \relax (x)}{\ln \relax (3)}+\frac {x^2\,\ln \relax (x)\,\left (20\,\ln \relax (3)-32\right )}{\ln \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 32, normalized size = 1.23 \begin {gather*} \frac {\left (4 x^{3} - 32 x^{2} + 20 x^{2} \log {\relax (3 )} + 28 x\right ) \log {\relax (x )}}{\log {\relax (3 )}} - 20 \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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