Optimal. Leaf size=25 \[ 2+\log (x)-\frac {1}{25} x^2 \left (6+x^2-\frac {3 \log (x)}{x}\right )^2 \]
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Rubi [A] time = 0.07, antiderivative size = 48, normalized size of antiderivative = 1.92, number of steps used = 10, number of rules used = 6, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {12, 14, 2357, 2295, 2301, 2304} \begin {gather*} -\frac {x^6}{25}-\frac {12 x^4}{25}+\frac {6}{25} x^3 \log (x)-\frac {36 x^2}{25}-\frac {9 \log ^2(x)}{25}+\frac {36}{25} x \log (x)+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2295
Rule 2301
Rule 2304
Rule 2357
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{25} \int \frac {25+36 x-72 x^2+6 x^3-48 x^4-6 x^6+\left (-18+36 x+18 x^3\right ) \log (x)}{x} \, dx\\ &=\frac {1}{25} \int \left (\frac {25+36 x-72 x^2+6 x^3-48 x^4-6 x^6}{x}+\frac {18 \left (-1+2 x+x^3\right ) \log (x)}{x}\right ) \, dx\\ &=\frac {1}{25} \int \frac {25+36 x-72 x^2+6 x^3-48 x^4-6 x^6}{x} \, dx+\frac {18}{25} \int \frac {\left (-1+2 x+x^3\right ) \log (x)}{x} \, dx\\ &=\frac {1}{25} \int \left (36+\frac {25}{x}-72 x+6 x^2-48 x^3-6 x^5\right ) \, dx+\frac {18}{25} \int \left (2 \log (x)-\frac {\log (x)}{x}+x^2 \log (x)\right ) \, dx\\ &=\frac {36 x}{25}-\frac {36 x^2}{25}+\frac {2 x^3}{25}-\frac {12 x^4}{25}-\frac {x^6}{25}+\log (x)-\frac {18}{25} \int \frac {\log (x)}{x} \, dx+\frac {18}{25} \int x^2 \log (x) \, dx+\frac {36}{25} \int \log (x) \, dx\\ &=-\frac {36 x^2}{25}-\frac {12 x^4}{25}-\frac {x^6}{25}+\log (x)+\frac {36}{25} x \log (x)+\frac {6}{25} x^3 \log (x)-\frac {9 \log ^2(x)}{25}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 48, normalized size = 1.92 \begin {gather*} -\frac {36 x^2}{25}-\frac {12 x^4}{25}-\frac {x^6}{25}+\log (x)+\frac {36}{25} x \log (x)+\frac {6}{25} x^3 \log (x)-\frac {9 \log ^2(x)}{25} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 36, normalized size = 1.44 \begin {gather*} -\frac {1}{25} \, x^{6} - \frac {12}{25} \, x^{4} - \frac {36}{25} \, x^{2} + \frac {1}{25} \, {\left (6 \, x^{3} + 36 \, x + 25\right )} \log \relax (x) - \frac {9}{25} \, \log \relax (x)^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 35, normalized size = 1.40 \begin {gather*} -\frac {1}{25} \, x^{6} - \frac {12}{25} \, x^{4} - \frac {36}{25} \, x^{2} + \frac {6}{25} \, {\left (x^{3} + 6 \, x\right )} \log \relax (x) - \frac {9}{25} \, \log \relax (x)^{2} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 37, normalized size = 1.48
method | result | size |
default | \(-\frac {x^{6}}{25}+\frac {6 x^{3} \ln \relax (x )}{25}-\frac {12 x^{4}}{25}+\frac {36 x \ln \relax (x )}{25}-\frac {36 x^{2}}{25}-\frac {9 \ln \relax (x )^{2}}{25}+\ln \relax (x )\) | \(37\) |
norman | \(-\frac {x^{6}}{25}+\frac {6 x^{3} \ln \relax (x )}{25}-\frac {12 x^{4}}{25}+\frac {36 x \ln \relax (x )}{25}-\frac {36 x^{2}}{25}-\frac {9 \ln \relax (x )^{2}}{25}+\ln \relax (x )\) | \(37\) |
risch | \(-\frac {9 \ln \relax (x )^{2}}{25}+\frac {\left (6 x^{3}+36 x \right ) \ln \relax (x )}{25}-\frac {x^{6}}{25}-\frac {12 x^{4}}{25}-\frac {36 x^{2}}{25}+\ln \relax (x )\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 36, normalized size = 1.44 \begin {gather*} -\frac {1}{25} \, x^{6} - \frac {12}{25} \, x^{4} + \frac {6}{25} \, x^{3} \log \relax (x) - \frac {36}{25} \, x^{2} + \frac {36}{25} \, x \log \relax (x) - \frac {9}{25} \, \log \relax (x)^{2} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 8.25, size = 36, normalized size = 1.44 \begin {gather*} -\frac {x^6}{25}-\frac {12\,x^4}{25}+\frac {6\,x^3\,\ln \relax (x)}{25}-\frac {36\,x^2}{25}+\frac {36\,x\,\ln \relax (x)}{25}-\frac {9\,{\ln \relax (x)}^2}{25}+\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 44, normalized size = 1.76 \begin {gather*} - \frac {x^{6}}{25} - \frac {12 x^{4}}{25} - \frac {36 x^{2}}{25} + \left (\frac {6 x^{3}}{25} + \frac {36 x}{25}\right ) \log {\relax (x )} - \frac {9 \log {\relax (x )}^{2}}{25} + \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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