Optimal. Leaf size=26 \[ -x+2 x^2-4 \left (x+x^2\right )^2 \log (3)+e^3 \log (x) \]
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Rubi [A]
time = 0.01, antiderivative size = 35, normalized size of antiderivative = 1.35, number of steps
used = 2, number of rules used = 1, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {14}
\begin {gather*} -4 x^4 \log (3)-8 x^3 \log (3)+2 x^2 (1-\log (9))-x+e^3 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1+\frac {e^3}{x}-24 x^2 \log (3)-16 x^3 \log (3)+4 x (1-\log (9))\right ) \, dx\\ &=-x-8 x^3 \log (3)-4 x^4 \log (3)+2 x^2 (1-\log (9))+e^3 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 36, normalized size = 1.38 \begin {gather*} -x+2 x^2-4 x^2 \log (3)-8 x^3 \log (3)-4 x^4 \log (3)+e^3 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.18, size = 36, normalized size = 1.38
method | result | size |
norman | \(\left (-4 \ln \left (3\right )+2\right ) x^{2}-x -8 x^{3} \ln \left (3\right )-4 x^{4} \ln \left (3\right )+\ln \left (x \right ) {\mathrm e}^{3}\) | \(34\) |
default | \(-4 x^{4} \ln \left (3\right )-8 x^{3} \ln \left (3\right )-4 x^{2} \ln \left (3\right )+2 x^{2}-x +\ln \left (x \right ) {\mathrm e}^{3}\) | \(36\) |
risch | \(-4 x^{4} \ln \left (3\right )-8 x^{3} \ln \left (3\right )-4 x^{2} \ln \left (3\right )+2 x^{2}-x +\ln \left (x \right ) {\mathrm e}^{3}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 34, normalized size = 1.31 \begin {gather*} -4 \, x^{4} \log \left (3\right ) - 8 \, x^{3} \log \left (3\right ) - 2 \, x^{2} {\left (2 \, \log \left (3\right ) - 1\right )} + e^{3} \log \left (x\right ) - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 30, normalized size = 1.15 \begin {gather*} 2 \, x^{2} - 4 \, {\left (x^{4} + 2 \, x^{3} + x^{2}\right )} \log \left (3\right ) + e^{3} \log \left (x\right ) - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 34, normalized size = 1.31 \begin {gather*} - 4 x^{4} \log {\left (3 \right )} - 8 x^{3} \log {\left (3 \right )} - x^{2} \left (-2 + 4 \log {\left (3 \right )}\right ) - x + e^{3} \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.37, size = 36, normalized size = 1.38 \begin {gather*} -4 \, x^{4} \log \left (3\right ) - 8 \, x^{3} \log \left (3\right ) - 4 \, x^{2} \log \left (3\right ) + 2 \, x^{2} + e^{3} \log \left ({\left | x \right |}\right ) - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 34, normalized size = 1.31 \begin {gather*} {\mathrm {e}}^3\,\ln \left (x\right )-x^2\,\left (4\,\ln \left (3\right )-2\right )-8\,x^3\,\ln \left (3\right )-4\,x^4\,\ln \left (3\right )-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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