Optimal. Leaf size=22 \[ \log (2) \log \left (-3+\frac {1}{x}+3 x-\left (e^e-x\right ) x\right ) \]
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Rubi [A] time = 0.21, antiderivative size = 30, normalized size of antiderivative = 1.36, number of steps used = 4, number of rules used = 3, integrand size = 54, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {6, 2074, 1587} \begin {gather*} \log (2) \log \left (x^3+\left (3-e^e\right ) x^2-3 x+1\right )-\log (2) \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 1587
Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^e x^2 \log (2)+\left (1-3 x^2-2 x^3\right ) \log (2)}{-x+3 x^2+\left (-3+e^e\right ) x^3-x^4} \, dx\\ &=\int \left (-\frac {\log (2)}{x}+\frac {\left (-3+2 \left (3-e^e\right ) x+3 x^2\right ) \log (2)}{1-3 x+\left (3-e^e\right ) x^2+x^3}\right ) \, dx\\ &=-\log (2) \log (x)+\log (2) \int \frac {-3+2 \left (3-e^e\right ) x+3 x^2}{1-3 x+\left (3-e^e\right ) x^2+x^3} \, dx\\ &=-\log (2) \log (x)+\log (2) \log \left (1-3 x+\left (3-e^e\right ) x^2+x^3\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 30, normalized size = 1.36 \begin {gather*} \log (2) \left (-\log (x)+\log \left (1-3 x+3 x^2-e^e x^2+x^3\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 32, normalized size = 1.45 \begin {gather*} \log \relax (2) \log \left (x^{3} - x^{2} e^{e} + 3 \, x^{2} - 3 \, x + 1\right ) - \log \relax (2) \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.39, size = 34, normalized size = 1.55 \begin {gather*} \log \relax (2) \log \left ({\left | x^{3} - x^{2} e^{e} + 3 \, x^{2} - 3 \, x + 1 \right |}\right ) - \log \relax (2) \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 31, normalized size = 1.41
method | result | size |
default | \(\ln \relax (2) \left (\ln \left (-x^{2} {\mathrm e}^{{\mathrm e}}+x^{3}+3 x^{2}-3 x +1\right )-\ln \relax (x )\right )\) | \(31\) |
risch | \(-\ln \relax (2) \ln \relax (x )+\ln \relax (2) \ln \left (1+x^{3}+\left (3-{\mathrm e}^{{\mathrm e}}\right ) x^{2}-3 x \right )\) | \(31\) |
norman | \(\ln \relax (2) \ln \left (x^{2} {\mathrm e}^{{\mathrm e}}-x^{3}-3 x^{2}+3 x -1\right )-\ln \relax (2) \ln \relax (x )\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 29, normalized size = 1.32 \begin {gather*} \log \relax (2) \log \left (x^{3} - x^{2} {\left (e^{e} - 3\right )} - 3 \, x + 1\right ) - \log \relax (2) \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.87, size = 30, normalized size = 1.36 \begin {gather*} \ln \relax (2)\,\left (\ln \left (3\,x^2-x^2\,{\mathrm {e}}^{\mathrm {e}}-3\,x+x^3+1\right )-\ln \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.28, size = 29, normalized size = 1.32 \begin {gather*} - \log {\relax (2 )} \log {\relax (x )} + \log {\relax (2 )} \log {\left (x^{3} + x^{2} \left (3 - e^{e}\right ) - 3 x + 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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