Optimal. Leaf size=22 \[ -x+\log \left (-e^x+\frac {3}{x^2}+\log \left (4 e^e\right )\right ) \]
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Rubi [F] time = 0.80, 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 {-6-3 x-x^3 \log \left (4 e^e\right )}{3 x-e^x x^3+x^3 \log \left (4 e^e\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-6-3 x-x^3 (e+\log (4))}{3 x-e^x x^3+x^3 \log \left (4 e^e\right )} \, dx\\ &=\int \left (\frac {3}{-3+e^x x^2-e x^2 \left (1+\frac {\log (4)}{e}\right )}+\frac {6}{x \left (-3+e^x x^2-e x^2 \left (1+\frac {\log (4)}{e}\right )\right )}+\frac {x^2 (-e-\log (4))}{3-e^x x^2+e x^2 \left (1+\frac {\log (4)}{e}\right )}\right ) \, dx\\ &=3 \int \frac {1}{-3+e^x x^2-e x^2 \left (1+\frac {\log (4)}{e}\right )} \, dx+6 \int \frac {1}{x \left (-3+e^x x^2-e x^2 \left (1+\frac {\log (4)}{e}\right )\right )} \, dx+(-e-\log (4)) \int \frac {x^2}{3-e^x x^2+e x^2 \left (1+\frac {\log (4)}{e}\right )} \, dx\\ &=3 \int \frac {1}{-3+e^x x^2-e x^2 \left (1+\frac {\log (4)}{e}\right )} \, dx+6 \int \frac {1}{-3 x-x^3 \left (e-e^x+\log (4)\right )} \, dx+(-e-\log (4)) \int \frac {x^2}{3-e^x x^2+e x^2 \left (1+\frac {\log (4)}{e}\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.22, size = 30, normalized size = 1.36 \begin {gather*} -x-2 \log (x)+\log \left (3+e x^2-e^x x^2+x^2 \log (4)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 32, normalized size = 1.45 \begin {gather*} -x + \log \left (-\frac {x^{2} e - x^{2} e^{x} + 2 \, x^{2} \log \relax (2) + 3}{x^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.31, size = 31, normalized size = 1.41 \begin {gather*} -x + \log \left (x^{2} e - x^{2} e^{x} + 2 \, x^{2} \log \relax (2) + 3\right ) - 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 29, normalized size = 1.32
method | result | size |
risch | \(-x +\ln \left ({\mathrm e}^{x}-\frac {x^{2} {\mathrm e}+2 x^{2} \ln \relax (2)+3}{x^{2}}\right )\) | \(29\) |
norman | \(-x -2 \ln \relax (x )+\ln \left (x^{2} {\mathrm e}-{\mathrm e}^{x} x^{2}+2 x^{2} \ln \relax (2)+3\right )\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.66, size = 30, normalized size = 1.36 \begin {gather*} -x + \log \left (-\frac {x^{2} {\left (e + 2 \, \log \relax (2)\right )} - x^{2} e^{x} + 3}{x^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.27, size = 31, normalized size = 1.41 \begin {gather*} \ln \left (\frac {x^2\,\mathrm {e}-x^2\,{\mathrm {e}}^x+2\,x^2\,\ln \relax (2)+3}{x^2}\right )-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 27, normalized size = 1.23 \begin {gather*} - x + \log {\left (e^{x} + \frac {- e x^{2} - 2 x^{2} \log {\relax (2 )} - 3}{x^{2}} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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