Optimal. Leaf size=28 \[ 2-x-\log \left (x-x^2 \left (-e^{e^5}+x^2+\log (x)\right )\right ) \]
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Rubi [F] time = 0.78, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {1-4 x^3-x^4+e^{e^5} \left (2 x+x^2\right )+\left (-2 x-x^2\right ) \log (x)}{-x-e^{e^5} x^2+x^4+x^2 \log (x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {-2-x}{x}-\frac {1+x+2 x^3}{x \left (-1-e^{e^5} x+x^3+x \log (x)\right )}\right ) \, dx\\ &=\int \frac {-2-x}{x} \, dx-\int \frac {1+x+2 x^3}{x \left (-1-e^{e^5} x+x^3+x \log (x)\right )} \, dx\\ &=\int \left (-1-\frac {2}{x}\right ) \, dx-\int \left (-\frac {1}{1+e^{e^5} x-x^3-x \log (x)}+\frac {1}{x \left (-1-e^{e^5} x+x^3+x \log (x)\right )}+\frac {2 x^2}{-1-e^{e^5} x+x^3+x \log (x)}\right ) \, dx\\ &=-x-2 \log (x)-2 \int \frac {x^2}{-1-e^{e^5} x+x^3+x \log (x)} \, dx+\int \frac {1}{1+e^{e^5} x-x^3-x \log (x)} \, dx-\int \frac {1}{x \left (-1-e^{e^5} x+x^3+x \log (x)\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.24, size = 30, normalized size = 1.07 \begin {gather*} -x-\log (x)-\log \left (1+e^{e^5} x-x^3-x \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 30, normalized size = 1.07 \begin {gather*} -x - 2 \, \log \relax (x) - \log \left (\frac {x^{3} - x e^{\left (e^{5}\right )} + x \log \relax (x) - 1}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.46, size = 26, normalized size = 0.93 \begin {gather*} -x - \log \left (x^{3} - x e^{\left (e^{5}\right )} + x \log \relax (x) - 1\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 29, normalized size = 1.04
method | result | size |
norman | \(-\ln \relax (x )-x -\ln \left (-x^{3}+x \,{\mathrm e}^{{\mathrm e}^{5}}-x \ln \relax (x )+1\right )\) | \(29\) |
risch | \(-x -2 \ln \relax (x )-\ln \left (\ln \relax (x )-\frac {-x^{3}+x \,{\mathrm e}^{{\mathrm e}^{5}}+1}{x}\right )\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 30, normalized size = 1.07 \begin {gather*} -x - 2 \, \log \relax (x) - \log \left (\frac {x^{3} - x e^{\left (e^{5}\right )} + x \log \relax (x) - 1}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.59, size = 34, normalized size = 1.21 \begin {gather*} -\ln \left (x\,\ln \relax (x)-x\,{\mathrm {e}}^{{\mathrm {e}}^5}+x^3-1\right )-\frac {x^2\,\ln \relax (x)+x^3}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 26, normalized size = 0.93 \begin {gather*} - x - 2 \log {\relax (x )} - \log {\left (\log {\relax (x )} + \frac {x^{3} - x e^{e^{5}} - 1}{x} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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