Optimal. Leaf size=26 \[ \log \left (3 e^{\left (-3+(-2+x)^2-x+\frac {5}{x^2 \log ^2(3)}\right )^2}\right ) \]
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Rubi [A] time = 0.03, antiderivative size = 44, normalized size of antiderivative = 1.69, number of steps used = 3, number of rules used = 2, integrand size = 52, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {12, 14} \begin {gather*} x^4+\frac {25}{x^4 \log ^4(3)}-10 x^3+27 x^2+\frac {10}{x^2 \log ^2(3)}-10 x-\frac {50}{x \log ^2(3)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-100+\left (-20 x^2+50 x^3\right ) \log ^2(3)+\left (-10 x^5+54 x^6-30 x^7+4 x^8\right ) \log ^4(3)}{x^5} \, dx}{\log ^4(3)}\\ &=\frac {\int \left (-\frac {100}{x^5}-\frac {20 \log ^2(3)}{x^3}+\frac {50 \log ^2(3)}{x^2}-10 \log ^4(3)+54 x \log ^4(3)-30 x^2 \log ^4(3)+4 x^3 \log ^4(3)\right ) \, dx}{\log ^4(3)}\\ &=-10 x+27 x^2-10 x^3+x^4+\frac {25}{x^4 \log ^4(3)}+\frac {10}{x^2 \log ^2(3)}-\frac {50}{x \log ^2(3)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 44, normalized size = 1.69 \begin {gather*} -10 x+27 x^2-10 x^3+x^4+\frac {25}{x^4 \log ^4(3)}+\frac {10}{x^2 \log ^2(3)}-\frac {50}{x \log ^2(3)} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.72, size = 51, normalized size = 1.96 \begin {gather*} \frac {{\left (x^{8} - 10 \, x^{7} + 27 \, x^{6} - 10 \, x^{5}\right )} \log \relax (3)^{4} - 10 \, {\left (5 \, x^{3} - x^{2}\right )} \log \relax (3)^{2} + 25}{x^{4} \log \relax (3)^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.21, size = 64, normalized size = 2.46 \begin {gather*} \frac {x^{4} \log \relax (3)^{4} - 10 \, x^{3} \log \relax (3)^{4} + 27 \, x^{2} \log \relax (3)^{4} - 10 \, x \log \relax (3)^{4} - \frac {5 \, {\left (10 \, x^{3} \log \relax (3)^{2} - 2 \, x^{2} \log \relax (3)^{2} - 5\right )}}{x^{4}}}{\log \relax (3)^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 46, normalized size = 1.77
method | result | size |
risch | \(x^{4}-10 x^{3}+27 x^{2}-10 x +\frac {-50 x^{3} \ln \relax (3)^{2}+10 x^{2} \ln \relax (3)^{2}+25}{\ln \relax (3)^{4} x^{4}}\) | \(46\) |
default | \(\frac {x^{4} \ln \relax (3)^{4}-10 \ln \relax (3)^{4} x^{3}+27 x^{2} \ln \relax (3)^{4}-10 x \ln \relax (3)^{4}+\frac {25}{x^{4}}-\frac {50 \ln \relax (3)^{2}}{x}+\frac {10 \ln \relax (3)^{2}}{x^{2}}}{\ln \relax (3)^{4}}\) | \(63\) |
gosper | \(\frac {x^{8} \ln \relax (3)^{4}-10 \ln \relax (3)^{4} x^{7}+27 x^{6} \ln \relax (3)^{4}-10 x^{5} \ln \relax (3)^{4}-50 x^{3} \ln \relax (3)^{2}+10 x^{2} \ln \relax (3)^{2}+25}{\ln \relax (3)^{4} x^{4}}\) | \(64\) |
norman | \(\frac {\ln \relax (3)^{3} x^{8}+\frac {25}{\ln \relax (3)}+10 x^{2} \ln \relax (3)-50 x^{3} \ln \relax (3)-10 \ln \relax (3)^{3} x^{5}+27 \ln \relax (3)^{3} x^{6}-10 \ln \relax (3)^{3} x^{7}}{x^{4} \ln \relax (3)^{3}}\) | \(65\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.36, size = 64, normalized size = 2.46 \begin {gather*} \frac {x^{4} \log \relax (3)^{4} - 10 \, x^{3} \log \relax (3)^{4} + 27 \, x^{2} \log \relax (3)^{4} - 10 \, x \log \relax (3)^{4} - \frac {5 \, {\left (10 \, x^{3} \log \relax (3)^{2} - 2 \, x^{2} \log \relax (3)^{2} - 5\right )}}{x^{4}}}{\log \relax (3)^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 45, normalized size = 1.73 \begin {gather*} 27\,x^2-10\,x-10\,x^3+x^4+\frac {-50\,{\ln \relax (3)}^2\,x^3+10\,{\ln \relax (3)}^2\,x^2+25}{x^4\,{\ln \relax (3)}^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.23, size = 66, normalized size = 2.54 \begin {gather*} \frac {x^{4} \log {\relax (3 )}^{4} - 10 x^{3} \log {\relax (3 )}^{4} + 27 x^{2} \log {\relax (3 )}^{4} - 10 x \log {\relax (3 )}^{4} + \frac {- 50 x^{3} \log {\relax (3 )}^{2} + 10 x^{2} \log {\relax (3 )}^{2} + 25}{x^{4}}}{\log {\relax (3 )}^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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