Optimal. Leaf size=26 \[ 4-\frac {3+x^2}{2+e^{-\frac {-7+x}{x^2}} \log (x)} \]
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Rubi [F] time = 20.64, 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 {-4 e^{\frac {2 (-7+x)}{x^2}} x^4+e^{\frac {-7+x}{x^2}} \left (3 x^2+x^4\right )+e^{\frac {-7+x}{x^2}} \left (-42+3 x-14 x^2+x^3-2 x^4\right ) \log (x)}{4 e^{\frac {2 (-7+x)}{x^2}} x^3+4 e^{\frac {-7+x}{x^2}} x^3 \log (x)+x^3 \log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {14}{x^2}} \left (-4 e^{\frac {2 (-7+x)}{x^2}} x^4+e^{\frac {-7+x}{x^2}} \left (3 x^2+x^4\right )+e^{\frac {-7+x}{x^2}} \left (-42+3 x-14 x^2+x^3-2 x^4\right ) \log (x)\right )}{x^3 \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )^2} \, dx\\ &=\int \left (-x-\frac {e^{\frac {14}{x^2}} \left (3+x^2\right ) \log (x) \left (x^2-14 \log (x)+x \log (x)\right )}{2 x^3 \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )^2}+\frac {e^{\frac {7}{x^2}} \left (3 x^2+x^4-42 \log (x)+3 x \log (x)-14 x^2 \log (x)+x^3 \log (x)+2 x^4 \log (x)\right )}{2 x^3 \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )}\right ) \, dx\\ &=-\frac {x^2}{2}-\frac {1}{2} \int \frac {e^{\frac {14}{x^2}} \left (3+x^2\right ) \log (x) \left (x^2-14 \log (x)+x \log (x)\right )}{x^3 \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )^2} \, dx+\frac {1}{2} \int \frac {e^{\frac {7}{x^2}} \left (3 x^2+x^4-42 \log (x)+3 x \log (x)-14 x^2 \log (x)+x^3 \log (x)+2 x^4 \log (x)\right )}{x^3 \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )} \, dx\\ &=-\frac {x^2}{2}+\frac {1}{2} \int \left (\frac {3 e^{\frac {7}{x^2}}}{x \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )}+\frac {e^{\frac {7}{x^2}} x}{2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)}+\frac {e^{\frac {7}{x^2}} \log (x)}{2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)}-\frac {42 e^{\frac {7}{x^2}} \log (x)}{x^3 \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )}+\frac {3 e^{\frac {7}{x^2}} \log (x)}{x^2 \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )}-\frac {14 e^{\frac {7}{x^2}} \log (x)}{x \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )}+\frac {2 e^{\frac {7}{x^2}} x \log (x)}{2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)}\right ) \, dx-\frac {1}{2} \int \left (\frac {3 e^{\frac {14}{x^2}} \log (x) \left (x^2-14 \log (x)+x \log (x)\right )}{x^3 \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )^2}+\frac {e^{\frac {14}{x^2}} \log (x) \left (x^2-14 \log (x)+x \log (x)\right )}{x \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )^2}\right ) \, dx\\ &=-\frac {x^2}{2}+\frac {1}{2} \int \frac {e^{\frac {7}{x^2}} x}{2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)} \, dx+\frac {1}{2} \int \frac {e^{\frac {7}{x^2}} \log (x)}{2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)} \, dx-\frac {1}{2} \int \frac {e^{\frac {14}{x^2}} \log (x) \left (x^2-14 \log (x)+x \log (x)\right )}{x \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )^2} \, dx+\frac {3}{2} \int \frac {e^{\frac {7}{x^2}}}{x \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )} \, dx+\frac {3}{2} \int \frac {e^{\frac {7}{x^2}} \log (x)}{x^2 \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )} \, dx-\frac {3}{2} \int \frac {e^{\frac {14}{x^2}} \log (x) \left (x^2-14 \log (x)+x \log (x)\right )}{x^3 \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )^2} \, dx-7 \int \frac {e^{\frac {7}{x^2}} \log (x)}{x \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )} \, dx-21 \int \frac {e^{\frac {7}{x^2}} \log (x)}{x^3 \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )} \, dx+\int \frac {e^{\frac {7}{x^2}} x \log (x)}{2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)} \, dx\\ &=-\frac {x^2}{2}+\frac {1}{2} \int \frac {e^{\frac {7}{x^2}} x}{2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)} \, dx+\frac {1}{2} \int \frac {e^{\frac {7}{x^2}} \log (x)}{2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)} \, dx-\frac {1}{2} \int \left (\frac {e^{\frac {14}{x^2}} x \log (x)}{\left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )^2}+\frac {e^{\frac {14}{x^2}} \log ^2(x)}{\left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )^2}-\frac {14 e^{\frac {14}{x^2}} \log ^2(x)}{x \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )^2}\right ) \, dx+\frac {3}{2} \int \frac {e^{\frac {7}{x^2}}}{x \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )} \, dx+\frac {3}{2} \int \frac {e^{\frac {7}{x^2}} \log (x)}{x^2 \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )} \, dx-\frac {3}{2} \int \left (\frac {e^{\frac {14}{x^2}} \log (x)}{x \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )^2}-\frac {14 e^{\frac {14}{x^2}} \log ^2(x)}{x^3 \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )^2}+\frac {e^{\frac {14}{x^2}} \log ^2(x)}{x^2 \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )^2}\right ) \, dx-7 \int \frac {e^{\frac {7}{x^2}} \log (x)}{x \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )} \, dx-21 \int \frac {e^{\frac {7}{x^2}} \log (x)}{x^3 \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )} \, dx+\int \frac {e^{\frac {7}{x^2}} x \log (x)}{2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)} \, dx\\ &=-\frac {x^2}{2}-\frac {1}{2} \int \frac {e^{\frac {14}{x^2}} x \log (x)}{\left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )^2} \, dx-\frac {1}{2} \int \frac {e^{\frac {14}{x^2}} \log ^2(x)}{\left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )^2} \, dx+\frac {1}{2} \int \frac {e^{\frac {7}{x^2}} x}{2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)} \, dx+\frac {1}{2} \int \frac {e^{\frac {7}{x^2}} \log (x)}{2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)} \, dx-\frac {3}{2} \int \frac {e^{\frac {14}{x^2}} \log (x)}{x \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )^2} \, dx-\frac {3}{2} \int \frac {e^{\frac {14}{x^2}} \log ^2(x)}{x^2 \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )^2} \, dx+\frac {3}{2} \int \frac {e^{\frac {7}{x^2}}}{x \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )} \, dx+\frac {3}{2} \int \frac {e^{\frac {7}{x^2}} \log (x)}{x^2 \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )} \, dx+7 \int \frac {e^{\frac {14}{x^2}} \log ^2(x)}{x \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )^2} \, dx-7 \int \frac {e^{\frac {7}{x^2}} \log (x)}{x \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )} \, dx+21 \int \frac {e^{\frac {14}{x^2}} \log ^2(x)}{x^3 \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )^2} \, dx-21 \int \frac {e^{\frac {7}{x^2}} \log (x)}{x^3 \left (2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)\right )} \, dx+\int \frac {e^{\frac {7}{x^2}} x \log (x)}{2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.09, size = 32, normalized size = 1.23 \begin {gather*} -\frac {e^{\frac {1}{x}} \left (3+x^2\right )}{2 e^{\frac {1}{x}}+e^{\frac {7}{x^2}} \log (x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.10, size = 30, normalized size = 1.15 \begin {gather*} -\frac {{\left (x^{2} + 3\right )} e^{\left (\frac {x - 7}{x^{2}}\right )}}{2 \, e^{\left (\frac {x - 7}{x^{2}}\right )} + \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.39, size = 35, normalized size = 1.35 \begin {gather*} -\frac {2 \, x^{2} e^{\left (\frac {x - 7}{x^{2}}\right )} - 3 \, \log \relax (x)}{2 \, {\left (2 \, e^{\left (\frac {x - 7}{x^{2}}\right )} + \log \relax (x)\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 31, normalized size = 1.19
method | result | size |
risch | \(-\frac {\left (x^{2}+3\right ) {\mathrm e}^{\frac {x -7}{x^{2}}}}{\ln \relax (x )+2 \,{\mathrm e}^{\frac {x -7}{x^{2}}}}\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 29, normalized size = 1.12 \begin {gather*} -\frac {{\left (x^{2} + 3\right )} e^{\frac {1}{x}}}{e^{\left (\frac {7}{x^{2}}\right )} \log \relax (x) + 2 \, e^{\frac {1}{x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.31, size = 36, normalized size = 1.38 \begin {gather*} \frac {\frac {3\,\ln \relax (x)}{2}+\frac {x^2\,\ln \relax (x)}{2}}{2\,{\mathrm {e}}^{\frac {1}{x}-\frac {7}{x^2}}+\ln \relax (x)}-\frac {x^2}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.33, size = 31, normalized size = 1.19 \begin {gather*} - \frac {x^{2}}{2} + \frac {x^{2} \log {\relax (x )} + 3 \log {\relax (x )}}{4 e^{\frac {x - 7}{x^{2}}} + 2 \log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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