Optimal. Leaf size=33 \[ \frac {5}{3 \left (2+e^{\frac {1}{x}}-e^{\frac {x^2 (x+x \log (2))}{\log (2)}}\right )}+x \]
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Rubi [F] time = 5.33, 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 {12 x^2 \log (2)+3 e^{2/x} x^2 \log (2)+3 e^{\frac {2 \left (x^3+x^3 \log (2)\right )}{\log (2)}} x^2 \log (2)+e^{\frac {1}{x}} \left (5+12 x^2\right ) \log (2)+e^{\frac {x^3+x^3 \log (2)}{\log (2)}} \left (15 x^4-6 e^{\frac {1}{x}} x^2 \log (2)+\left (-12 x^2+15 x^4\right ) \log (2)\right )}{12 x^2 \log (2)+12 e^{\frac {1}{x}} x^2 \log (2)+3 e^{2/x} x^2 \log (2)+3 e^{\frac {2 \left (x^3+x^3 \log (2)\right )}{\log (2)}} x^2 \log (2)+e^{\frac {x^3+x^3 \log (2)}{\log (2)}} \left (-12 x^2 \log (2)-6 e^{\frac {1}{x}} x^2 \log (2)\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 {12 x^2 \log (2)-6 e^{\frac {1}{x}+x^3 \left (1+\frac {1}{\log (2)}\right )} x^2 \log (2)+3 e^{2 x^3 \left (1+\frac {1}{\log (2)}\right )} x^2 \log (2)+3 e^{x^3 \left (1+\frac {1}{\log (2)}\right )} x^2 \left (-4 \log (2)+5 x^2 (1+\log (2))\right )+e^{2/x} x^2 \log (8)+e^{\frac {1}{x}} \left (12 x^2 \log (2)+\log (32)\right )}{3 \left (2+e^{\frac {1}{x}}-e^{x^3 \left (1+\frac {1}{\log (2)}\right )}\right )^2 x^2 \log (2)} \, dx\\ &=\frac {\int \frac {12 x^2 \log (2)-6 e^{\frac {1}{x}+x^3 \left (1+\frac {1}{\log (2)}\right )} x^2 \log (2)+3 e^{2 x^3 \left (1+\frac {1}{\log (2)}\right )} x^2 \log (2)+3 e^{x^3 \left (1+\frac {1}{\log (2)}\right )} x^2 \left (-4 \log (2)+5 x^2 (1+\log (2))\right )+e^{2/x} x^2 \log (8)+e^{\frac {1}{x}} \left (12 x^2 \log (2)+\log (32)\right )}{\left (2+e^{\frac {1}{x}}-e^{x^3 \left (1+\frac {1}{\log (2)}\right )}\right )^2 x^2} \, dx}{3 \log (2)}\\ &=\frac {\int \left (-\frac {15 x^2 (1+\log (2))}{2+e^{\frac {1}{x}}-e^{x^3 \left (1+\frac {1}{\log (2)}\right )}}+\log (8)+\frac {30 x^4 (1+\log (2))+15 e^{\frac {1}{x}} x^4 (1+\log (2))+e^{\frac {1}{x}} \log (32)}{\left (2+e^{\frac {1}{x}}-e^{x^3 \left (1+\frac {1}{\log (2)}\right )}\right )^2 x^2}\right ) \, dx}{3 \log (2)}\\ &=\frac {x \log (8)}{3 \log (2)}+\frac {\int \frac {30 x^4 (1+\log (2))+15 e^{\frac {1}{x}} x^4 (1+\log (2))+e^{\frac {1}{x}} \log (32)}{\left (2+e^{\frac {1}{x}}-e^{x^3 \left (1+\frac {1}{\log (2)}\right )}\right )^2 x^2} \, dx}{3 \log (2)}-\frac {(5 (1+\log (2))) \int \frac {x^2}{2+e^{\frac {1}{x}}-e^{x^3 \left (1+\frac {1}{\log (2)}\right )}} \, dx}{\log (2)}\\ &=\frac {x \log (8)}{3 \log (2)}+\frac {\int \left (\frac {30 x^2 (1+\log (2))}{\left (2+e^{\frac {1}{x}}-e^{x^3 \left (1+\frac {1}{\log (2)}\right )}\right )^2}+\frac {15 e^{\frac {1}{x}} x^2 (1+\log (2))}{\left (2+e^{\frac {1}{x}}-e^{x^3 \left (1+\frac {1}{\log (2)}\right )}\right )^2}+\frac {e^{\frac {1}{x}} \log (32)}{\left (2+e^{\frac {1}{x}}-e^{x^3 \left (1+\frac {1}{\log (2)}\right )}\right )^2 x^2}\right ) \, dx}{3 \log (2)}-\frac {(5 (1+\log (2))) \int \frac {x^2}{2+e^{\frac {1}{x}}-e^{x^3 \left (1+\frac {1}{\log (2)}\right )}} \, dx}{\log (2)}\\ &=\frac {x \log (8)}{3 \log (2)}+\frac {(5 (1+\log (2))) \int \frac {e^{\frac {1}{x}} x^2}{\left (2+e^{\frac {1}{x}}-e^{x^3 \left (1+\frac {1}{\log (2)}\right )}\right )^2} \, dx}{\log (2)}-\frac {(5 (1+\log (2))) \int \frac {x^2}{2+e^{\frac {1}{x}}-e^{x^3 \left (1+\frac {1}{\log (2)}\right )}} \, dx}{\log (2)}+\frac {(10 (1+\log (2))) \int \frac {x^2}{\left (2+e^{\frac {1}{x}}-e^{x^3 \left (1+\frac {1}{\log (2)}\right )}\right )^2} \, dx}{\log (2)}+\frac {\log (32) \int \frac {e^{\frac {1}{x}}}{\left (2+e^{\frac {1}{x}}-e^{x^3 \left (1+\frac {1}{\log (2)}\right )}\right )^2 x^2} \, dx}{3 \log (2)}\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.34, size = 86, normalized size = 2.61 \begin {gather*} \frac {1}{3} \left (3 x+\frac {15 \left (2+e^{\frac {1}{x}}\right ) x^4 (1+\log (2))+e^{\frac {1}{x}} \log (32)}{\left (2+e^{\frac {1}{x}}-e^{x^3 \left (1+\frac {1}{\log (2)}\right )}\right ) \left (e^{\frac {1}{x}} \log (2)+x^4 \left (6+e^{\frac {1}{x}} (3+\log (8))+\log (64)\right )\right )}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.64, size = 59, normalized size = 1.79 \begin {gather*} \frac {3 \, x e^{\left (\frac {x^{3} \log \relax (2) + x^{3}}{\log \relax (2)}\right )} - 3 \, x e^{\frac {1}{x}} - 6 \, x - 5}{3 \, {\left (e^{\left (\frac {x^{3} \log \relax (2) + x^{3}}{\log \relax (2)}\right )} - e^{\frac {1}{x}} - 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.29, size = 28, normalized size = 0.85
method | result | size |
risch | \(x +\frac {5}{3 \left ({\mathrm e}^{\frac {1}{x}}-{\mathrm e}^{\frac {x^{3} \left (1+\ln \relax (2)\right )}{\ln \relax (2)}}+2\right )}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 53, normalized size = 1.61 \begin {gather*} \frac {3 \, x e^{\left (x^{3} + \frac {x^{3}}{\log \relax (2)}\right )} - 3 \, x e^{\frac {1}{x}} - 6 \, x - 5}{3 \, {\left (e^{\left (x^{3} + \frac {x^{3}}{\log \relax (2)}\right )} - e^{\frac {1}{x}} - 2\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 {12\,x^2\,\ln \relax (2)-{\mathrm {e}}^{\frac {x^3\,\ln \relax (2)+x^3}{\ln \relax (2)}}\,\left (\ln \relax (2)\,\left (12\,x^2-15\,x^4\right )-15\,x^4+6\,x^2\,{\mathrm {e}}^{1/x}\,\ln \relax (2)\right )+3\,x^2\,{\mathrm {e}}^{\frac {2\,\left (x^3\,\ln \relax (2)+x^3\right )}{\ln \relax (2)}}\,\ln \relax (2)+3\,x^2\,{\mathrm {e}}^{2/x}\,\ln \relax (2)+{\mathrm {e}}^{1/x}\,\ln \relax (2)\,\left (12\,x^2+5\right )}{12\,x^2\,\ln \relax (2)-{\mathrm {e}}^{\frac {x^3\,\ln \relax (2)+x^3}{\ln \relax (2)}}\,\left (12\,x^2\,\ln \relax (2)+6\,x^2\,{\mathrm {e}}^{1/x}\,\ln \relax (2)\right )+3\,x^2\,{\mathrm {e}}^{\frac {2\,\left (x^3\,\ln \relax (2)+x^3\right )}{\ln \relax (2)}}\,\ln \relax (2)+3\,x^2\,{\mathrm {e}}^{2/x}\,\ln \relax (2)+12\,x^2\,{\mathrm {e}}^{1/x}\,\ln \relax (2)} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.37, size = 27, normalized size = 0.82 \begin {gather*} x - \frac {5}{- 3 e^{\frac {1}{x}} + 3 e^{\frac {x^{3} \log {\relax (2 )} + x^{3}}{\log {\relax (2 )}}} - 6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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