Optimal. Leaf size=20 \[ e^{1+\frac {4}{x}+x} \left (-4+\frac {x}{2}+\log (2)\right ) \]
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Rubi [F] time = 0.61, 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 {e^{\frac {4+x+x^2}{x}} \left (32-4 x-7 x^2+x^3+\left (-8+2 x^2\right ) \log (2)\right )}{2 x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \frac {e^{\frac {4+x+x^2}{x}} \left (32-4 x-7 x^2+x^3+\left (-8+2 x^2\right ) \log (2)\right )}{x^2} \, dx\\ &=\frac {1}{2} \int \frac {e^{1+\frac {4}{x}+x} \left (-4 x+x^3+8 (4-\log (2))-x^2 (7-\log (4))\right )}{x^2} \, dx\\ &=\frac {1}{2} \int \left (-\frac {4 e^{1+\frac {4}{x}+x}}{x}+e^{1+\frac {4}{x}+x} x-7 e^{1+\frac {4}{x}+x} \left (1-\frac {2 \log (2)}{7}\right )-\frac {8 e^{1+\frac {4}{x}+x} (-4+\log (2))}{x^2}\right ) \, dx\\ &=\frac {1}{2} \int e^{1+\frac {4}{x}+x} x \, dx-2 \int \frac {e^{1+\frac {4}{x}+x}}{x} \, dx+(4 (4-\log (2))) \int \frac {e^{1+\frac {4}{x}+x}}{x^2} \, dx+\frac {1}{2} (-7+\log (4)) \int e^{1+\frac {4}{x}+x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [F] time = 0.27, size = 45, normalized size = 2.25 \begin {gather*} \frac {1}{2} \int \frac {e^{\frac {4+x+x^2}{x}} \left (32-4 x-7 x^2+x^3+\left (-8+2 x^2\right ) \log (2)\right )}{x^2} \, dx \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 20, normalized size = 1.00 \begin {gather*} \frac {1}{2} \, {\left (x + 2 \, \log \relax (2) - 8\right )} e^{\left (\frac {x^{2} + x + 4}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.20, size = 42, normalized size = 2.10 \begin {gather*} \frac {1}{2} \, x e^{\left (\frac {x^{2} + x + 4}{x}\right )} + e^{\left (\frac {x^{2} + x + 4}{x}\right )} \log \relax (2) - 4 \, e^{\left (\frac {x^{2} + x + 4}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.15, size = 21, normalized size = 1.05
method | result | size |
gosper | \(\frac {{\mathrm e}^{\frac {x^{2}+x +4}{x}} \left (x +2 \ln \relax (2)-8\right )}{2}\) | \(21\) |
risch | \(\frac {{\mathrm e}^{\frac {x^{2}+x +4}{x}} \left (x +2 \ln \relax (2)-8\right )}{2}\) | \(21\) |
norman | \(\frac {x \left (\ln \relax (2)-4\right ) {\mathrm e}^{\frac {x^{2}+x +4}{x}}+\frac {x^{2} {\mathrm e}^{\frac {x^{2}+x +4}{x}}}{2}}{x}\) | \(39\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.67, size = 23, normalized size = 1.15 \begin {gather*} \frac {1}{2} \, {\left (x e + 2 \, {\left (\log \relax (2) - 4\right )} e\right )} e^{\left (x + \frac {4}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.67, size = 17, normalized size = 0.85 \begin {gather*} {\mathrm {e}}^{x+\frac {4}{x}+1}\,\left (\frac {x}{2}+\ln \relax (2)-4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.22, size = 19, normalized size = 0.95 \begin {gather*} \frac {\left (x - 8 + 2 \log {\relax (2 )}\right ) e^{\frac {x^{2} + x + 4}{x}}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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