Optimal. Leaf size=25 \[ -4-\left (3-e^e\right )^4 x^2-\log \left (x \log \left (\frac {1}{x}\right )\right ) \]
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Rubi [A] time = 0.32, antiderivative size = 26, normalized size of antiderivative = 1.04, number of steps used = 7, number of rules used = 4, integrand size = 62, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.065, Rules used = {6688, 14, 2302, 29} \begin {gather*} -\left (3-e^e\right )^4 x^2-\log (x)-\log \left (\log \left (\frac {1}{x}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 29
Rule 2302
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-1-2 \left (-3+e^e\right )^4 x^2+\frac {1}{\log \left (\frac {1}{x}\right )}}{x} \, dx\\ &=\int \left (\frac {-1-2 \left (3-e^e\right )^4 x^2}{x}+\frac {1}{x \log \left (\frac {1}{x}\right )}\right ) \, dx\\ &=\int \frac {-1-2 \left (3-e^e\right )^4 x^2}{x} \, dx+\int \frac {1}{x \log \left (\frac {1}{x}\right )} \, dx\\ &=\int \left (-\frac {1}{x}-2 \left (3-e^e\right )^4 x\right ) \, dx-\operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,\log \left (\frac {1}{x}\right )\right )\\ &=-\left (3-e^e\right )^4 x^2-\log (x)-\log \left (\log \left (\frac {1}{x}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.07, size = 24, normalized size = 0.96 \begin {gather*} -\left (-3+e^e\right )^4 x^2-\log (x)-\log \left (\log \left (\frac {1}{x}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.70, size = 55, normalized size = 2.20 \begin {gather*} -x^{2} e^{\left (4 \, e\right )} + 12 \, x^{2} e^{\left (3 \, e\right )} - 54 \, x^{2} e^{\left (2 \, e\right )} + 108 \, x^{2} e^{e} - 81 \, x^{2} + \log \left (\frac {1}{x}\right ) - \log \left (\log \left (\frac {1}{x}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.15, size = 53, normalized size = 2.12 \begin {gather*} -x^{2} e^{\left (4 \, e\right )} + 12 \, x^{2} e^{\left (3 \, e\right )} - 54 \, x^{2} e^{\left (2 \, e\right )} + 108 \, x^{2} e^{e} - 81 \, x^{2} - \log \relax (x) - \log \left (\log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 45, normalized size = 1.80
method | result | size |
norman | \(\ln \left (\frac {1}{x}\right )+\left (-{\mathrm e}^{4 \,{\mathrm e}}+12 \,{\mathrm e}^{3 \,{\mathrm e}}-54 \,{\mathrm e}^{2 \,{\mathrm e}}+108 \,{\mathrm e}^{{\mathrm e}}-81\right ) x^{2}-\ln \left (\ln \left (\frac {1}{x}\right )\right )\) | \(45\) |
derivativedivides | \(-x^{2} {\mathrm e}^{4 \,{\mathrm e}}+12 x^{2} {\mathrm e}^{3 \,{\mathrm e}}-54 x^{2} {\mathrm e}^{2 \,{\mathrm e}}+\ln \left (\frac {1}{x}\right )+108 x^{2} {\mathrm e}^{{\mathrm e}}-\ln \left (\ln \left (\frac {1}{x}\right )\right )-81 x^{2}\) | \(56\) |
default | \(-x^{2} {\mathrm e}^{4 \,{\mathrm e}}+12 x^{2} {\mathrm e}^{3 \,{\mathrm e}}-54 x^{2} {\mathrm e}^{2 \,{\mathrm e}}+\ln \left (\frac {1}{x}\right )+108 x^{2} {\mathrm e}^{{\mathrm e}}-\ln \left (\ln \left (\frac {1}{x}\right )\right )-81 x^{2}\) | \(56\) |
risch | \(-x^{2} {\mathrm e}^{4 \,{\mathrm e}}+12 x^{2} {\mathrm e}^{3 \,{\mathrm e}}-54 x^{2} {\mathrm e}^{2 \,{\mathrm e}}+108 x^{2} {\mathrm e}^{{\mathrm e}}-81 x^{2}-\ln \relax (x )-\ln \left (\ln \left (\frac {1}{x}\right )\right )\) | \(56\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.39, size = 53, normalized size = 2.12 \begin {gather*} -x^{2} e^{\left (4 \, e\right )} + 12 \, x^{2} e^{\left (3 \, e\right )} - 54 \, x^{2} e^{\left (2 \, e\right )} + 108 \, x^{2} e^{e} - 81 \, x^{2} - \log \relax (x) - \log \left (\log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.09, size = 33, normalized size = 1.32 \begin {gather*} \frac {x^2\,\ln \left (\frac {1}{x}\right )-x^4\,{\left ({\mathrm {e}}^{\mathrm {e}}-3\right )}^4}{x^2}-\ln \left (\ln \left (\frac {1}{x}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.19, size = 46, normalized size = 1.84 \begin {gather*} - x^{2} \left (- 12 e^{3 e} - 108 e^{e} + 81 + 54 e^{2 e} + e^{4 e}\right ) - \log {\relax (x )} - \log {\left (\log {\left (\frac {1}{x} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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