Optimal. Leaf size=25 \[ \frac {3 x}{2}-(2+x) \left (2+x+x^2+\frac {x^2}{\log ^2(3)}\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 34, normalized size of antiderivative = 1.36, number of steps used = 3, number of rules used = 1, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {12} \begin {gather*} -x^3-\frac {x^3}{\log ^2(3)}-3 x^2-\frac {2 x^2}{\log ^2(3)}-\frac {5 x}{2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (-8 x-6 x^2+\left (-5-12 x-6 x^2\right ) \log ^2(3)\right ) \, dx}{2 \log ^2(3)}\\ &=-\frac {2 x^2}{\log ^2(3)}-\frac {x^3}{\log ^2(3)}+\frac {1}{2} \int \left (-5-12 x-6 x^2\right ) \, dx\\ &=-\frac {5 x}{2}-3 x^2-x^3-\frac {2 x^2}{\log ^2(3)}-\frac {x^3}{\log ^2(3)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 34, normalized size = 1.36 \begin {gather*} -\frac {5 x}{2}-3 x^2-x^3-\frac {2 x^2}{\log ^2(3)}-\frac {x^3}{\log ^2(3)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.87, size = 36, normalized size = 1.44 \begin {gather*} -\frac {2 \, x^{3} + {\left (2 \, x^{3} + 6 \, x^{2} + 5 \, x\right )} \log \relax (3)^{2} + 4 \, x^{2}}{2 \, \log \relax (3)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.55, size = 36, normalized size = 1.44 \begin {gather*} -\frac {2 \, x^{3} + {\left (2 \, x^{3} + 6 \, x^{2} + 5 \, x\right )} \log \relax (3)^{2} + 4 \, x^{2}}{2 \, \log \relax (3)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 33, normalized size = 1.32
method | result | size |
risch | \(-x^{3}-3 x^{2}-\frac {5 x}{2}-\frac {x^{3}}{\ln \relax (3)^{2}}-\frac {2 x^{2}}{\ln \relax (3)^{2}}\) | \(33\) |
default | \(\frac {\ln \relax (3)^{2} \left (-2 x^{3}-6 x^{2}-5 x \right )-2 x^{3}-4 x^{2}}{2 \ln \relax (3)^{2}}\) | \(37\) |
gosper | \(-\frac {x \left (2 x^{2} \ln \relax (3)^{2}+6 x \ln \relax (3)^{2}+5 \ln \relax (3)^{2}+2 x^{2}+4 x \right )}{2 \ln \relax (3)^{2}}\) | \(39\) |
norman | \(\frac {-\frac {5 x \ln \relax (3)}{2}-\frac {\left (\ln \relax (3)^{2}+1\right ) x^{3}}{\ln \relax (3)}-\frac {\left (3 \ln \relax (3)^{2}+2\right ) x^{2}}{\ln \relax (3)}}{\ln \relax (3)}\) | \(44\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 36, normalized size = 1.44 \begin {gather*} -\frac {2 \, x^{3} + {\left (2 \, x^{3} + 6 \, x^{2} + 5 \, x\right )} \log \relax (3)^{2} + 4 \, x^{2}}{2 \, \log \relax (3)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.92, size = 38, normalized size = 1.52 \begin {gather*} -\frac {\left (6\,{\ln \relax (3)}^2+6\right )\,x^3}{6\,{\ln \relax (3)}^2}-\frac {\left (12\,{\ln \relax (3)}^2+8\right )\,x^2}{4\,{\ln \relax (3)}^2}-\frac {5\,x}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 39, normalized size = 1.56 \begin {gather*} \frac {x^{3} \left (- \log {\relax (3 )}^{2} - 1\right )}{\log {\relax (3 )}^{2}} + \frac {x^{2} \left (- 3 \log {\relax (3 )}^{2} - 2\right )}{\log {\relax (3 )}^{2}} - \frac {5 x}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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