Optimal. Leaf size=25 \[ 2 x \left (e^{\frac {\log ^2(x)}{9}}+3 x-\log ^2\left (x^2\right )\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 28, normalized size of antiderivative = 1.12, number of steps used = 6, number of rules used = 4, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {12, 2288, 2295, 2296} \begin {gather*} 6 x^2-2 x \log ^2\left (x^2\right )+2 x e^{\frac {\log ^2(x)}{9}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2288
Rule 2295
Rule 2296
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{9} \int \left (108 x+e^{\frac {\log ^2(x)}{9}} (18+4 \log (x))-72 \log \left (x^2\right )-18 \log ^2\left (x^2\right )\right ) \, dx\\ &=6 x^2+\frac {1}{9} \int e^{\frac {\log ^2(x)}{9}} (18+4 \log (x)) \, dx-2 \int \log ^2\left (x^2\right ) \, dx-8 \int \log \left (x^2\right ) \, dx\\ &=16 x+2 e^{\frac {\log ^2(x)}{9}} x+6 x^2-8 x \log \left (x^2\right )-2 x \log ^2\left (x^2\right )+8 \int \log \left (x^2\right ) \, dx\\ &=2 e^{\frac {\log ^2(x)}{9}} x+6 x^2-2 x \log ^2\left (x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 28, normalized size = 1.12 \begin {gather*} 2 e^{\frac {\log ^2(x)}{9}} x+6 x^2-2 x \log ^2\left (x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 23, normalized size = 0.92 \begin {gather*} -8 \, x \log \relax (x)^{2} + 6 \, x^{2} + 2 \, x e^{\left (\frac {1}{9} \, \log \relax (x)^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 25, normalized size = 1.00 \begin {gather*} -2 \, x \log \left (x^{2}\right )^{2} + 6 \, x^{2} + 2 \, x e^{\left (\frac {1}{9} \, \log \relax (x)^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 26, normalized size = 1.04
method | result | size |
default | \(6 x^{2}-2 x \ln \left (x^{2}\right )^{2}+2 \,{\mathrm e}^{\frac {\ln \relax (x )^{2}}{9}} x\) | \(26\) |
risch | \(6 x^{2}-2 x \ln \left (x^{2}\right )^{2}+2 \,{\mathrm e}^{\frac {\ln \relax (x )^{2}}{9}} x\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 25, normalized size = 1.00 \begin {gather*} -2 \, x \log \left (x^{2}\right )^{2} + 6 \, x^{2} + 2 \, x e^{\left (\frac {1}{9} \, \log \relax (x)^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.26, size = 22, normalized size = 0.88 \begin {gather*} 2\,x\,\left (-{\ln \left (x^2\right )}^2+3\,x+{\mathrm {e}}^{\frac {{\ln \relax (x)}^2}{9}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.28, size = 24, normalized size = 0.96 \begin {gather*} 6 x^{2} + 2 x e^{\frac {\log {\relax (x )}^{2}}{9}} - 8 x \log {\relax (x )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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