Optimal. Leaf size=30 \[ \log \left (\frac {1}{x+\frac {3 \left (e^x-x\right )^2 (3+x) (3-\log (x))}{16 x}}\right ) \]
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Rubi [F] time = 180.00, 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*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
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Aborted
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Mathematica [B] time = 0.25, size = 97, normalized size = 3.23 \begin {gather*} \log (x)-\log \left (-27 e^{2 x}+54 e^x x-9 e^{2 x} x-43 x^2+18 e^x x^2-9 x^3+9 e^{2 x} \log (x)-18 e^x x \log (x)+3 e^{2 x} x \log (x)+9 x^2 \log (x)-6 e^x x^2 \log (x)+3 x^3 \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.65, size = 116, normalized size = 3.87 \begin {gather*} -\log \left (x + 3\right ) + \log \relax (x) - 2 \, \log \left (-x + e^{x}\right ) - \log \left (-\frac {9 \, x^{3} + 43 \, x^{2} + 9 \, {\left (x + 3\right )} e^{\left (2 \, x\right )} - 18 \, {\left (x^{2} + 3 \, x\right )} e^{x} - 3 \, {\left (x^{3} + 3 \, x^{2} + {\left (x + 3\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x^{2} + 3 \, x\right )} e^{x}\right )} \log \relax (x)}{x^{3} + 3 \, x^{2} + {\left (x + 3\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x^{2} + 3 \, x\right )} e^{x}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.28, size = 89, normalized size = 2.97 \begin {gather*} -\log \left (3 \, x^{3} \log \relax (x) - 6 \, x^{2} e^{x} \log \relax (x) - 9 \, x^{3} + 18 \, x^{2} e^{x} + 9 \, x^{2} \log \relax (x) + 3 \, x e^{\left (2 \, x\right )} \log \relax (x) - 18 \, x e^{x} \log \relax (x) - 43 \, x^{2} - 9 \, x e^{\left (2 \, x\right )} + 54 \, x e^{x} + 9 \, e^{\left (2 \, x\right )} \log \relax (x) - 27 \, e^{\left (2 \, x\right )}\right ) + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.08, size = 98, normalized size = 3.27
method | result | size |
risch | \(\ln \relax (x )-\ln \left (3+x \right )-2 \ln \left ({\mathrm e}^{x}-x \right )-\ln \left (\ln \relax (x )-\frac {9 x^{3}-18 \,{\mathrm e}^{x} x^{2}+9 x \,{\mathrm e}^{2 x}+43 x^{2}-54 \,{\mathrm e}^{x} x +27 \,{\mathrm e}^{2 x}}{3 \left (x^{3}-2 \,{\mathrm e}^{x} x^{2}+x \,{\mathrm e}^{2 x}+3 x^{2}-6 \,{\mathrm e}^{x} x +3 \,{\mathrm e}^{2 x}\right )}\right )\) | \(98\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.48, size = 99, normalized size = 3.30 \begin {gather*} -\log \left (x + 3\right ) + \log \relax (x) - \log \left (-\frac {9 \, x^{3} + 43 \, x^{2} - 3 \, {\left ({\left (x + 3\right )} \log \relax (x) - 3 \, x - 9\right )} e^{\left (2 \, x\right )} - 6 \, {\left (3 \, x^{2} - {\left (x^{2} + 3 \, x\right )} \log \relax (x) + 9 \, x\right )} e^{x} - 3 \, {\left (x^{3} + 3 \, x^{2}\right )} \log \relax (x)}{3 \, {\left ({\left (x + 3\right )} \log \relax (x) - 3 \, x - 9\right )}}\right ) - \log \left (\log \relax (x) - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {{\mathrm {e}}^{2\,x}\,\left (18\,x^2+51\,x-36\right )-\ln \relax (x)\,\left ({\mathrm {e}}^{2\,x}\,\left (6\,x^2+18\,x-9\right )-{\mathrm {e}}^x\,\left (6\,x^3+24\,x^2\right )+9\,x^2+6\,x^3\right )+34\,x^2+15\,x^3-{\mathrm {e}}^x\,\left (18\,x^3+66\,x^2-18\,x\right )}{{\mathrm {e}}^{2\,x}\,\left (9\,x^2+27\,x\right )-{\mathrm {e}}^x\,\left (18\,x^3+54\,x^2\right )-\ln \relax (x)\,\left ({\mathrm {e}}^{2\,x}\,\left (3\,x^2+9\,x\right )-{\mathrm {e}}^x\,\left (6\,x^3+18\,x^2\right )+9\,x^3+3\,x^4\right )+43\,x^3+9\,x^4} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 5.92, size = 71, normalized size = 2.37 \begin {gather*} \log {\relax (x )} - \log {\left (x + 3 \right )} - \log {\left (\log {\relax (x )} - 3 \right )} - \log {\left (- 2 x e^{x} + e^{2 x} + \frac {3 x^{3} \log {\relax (x )} - 9 x^{3} + 9 x^{2} \log {\relax (x )} - 43 x^{2}}{3 x \log {\relax (x )} - 9 x + 9 \log {\relax (x )} - 27} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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