Optimal. Leaf size=28 \[ \left (e^{\frac {5}{-1+x}+\frac {x}{\log (x)}}+2 x\right ) \left (-x+x^2\right ) \]
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Rubi [F] time = 5.48, 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 {\left (4 x-10 x^2+6 x^3\right ) \log ^2(x)+e^{\frac {-x+x^2+5 \log (x)}{(-1+x) \log (x)}} \left (-x+2 x^2-x^3+\left (x-2 x^2+x^3\right ) \log (x)+\left (1-8 x+2 x^2\right ) \log ^2(x)\right )}{(-1+x) \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 \left (2 x (-2+3 x)+\frac {e^{\frac {5}{-1+x}+\frac {x}{\log (x)}} \left (-x+2 x^2-x^3+x \log (x)-2 x^2 \log (x)+x^3 \log (x)+\log ^2(x)-8 x \log ^2(x)+2 x^2 \log ^2(x)\right )}{(-1+x) \log ^2(x)}\right ) \, dx\\ &=2 \int x (-2+3 x) \, dx+\int \frac {e^{\frac {5}{-1+x}+\frac {x}{\log (x)}} \left (-x+2 x^2-x^3+x \log (x)-2 x^2 \log (x)+x^3 \log (x)+\log ^2(x)-8 x \log ^2(x)+2 x^2 \log ^2(x)\right )}{(-1+x) \log ^2(x)} \, dx\\ &=2 \int \left (-2 x+3 x^2\right ) \, dx+\int \frac {e^{\frac {5}{-1+x}+\frac {x}{\log (x)}} \left ((-1+x)^2 x-(-1+x)^2 x \log (x)-\left (1-8 x+2 x^2\right ) \log ^2(x)\right )}{(1-x) \log ^2(x)} \, dx\\ &=-2 x^2+2 x^3+\int \left (\frac {e^{\frac {5}{-1+x}+\frac {x}{\log (x)}} \left (1-8 x+2 x^2\right )}{-1+x}-\frac {e^{\frac {5}{-1+x}+\frac {x}{\log (x)}} (-1+x) x}{\log ^2(x)}+\frac {e^{\frac {5}{-1+x}+\frac {x}{\log (x)}} (-1+x) x}{\log (x)}\right ) \, dx\\ &=-2 x^2+2 x^3+\int \frac {e^{\frac {5}{-1+x}+\frac {x}{\log (x)}} \left (1-8 x+2 x^2\right )}{-1+x} \, dx-\int \frac {e^{\frac {5}{-1+x}+\frac {x}{\log (x)}} (-1+x) x}{\log ^2(x)} \, dx+\int \frac {e^{\frac {5}{-1+x}+\frac {x}{\log (x)}} (-1+x) x}{\log (x)} \, dx\\ &=-2 x^2+2 x^3+\int \left (-6 e^{\frac {5}{-1+x}+\frac {x}{\log (x)}}-\frac {5 e^{\frac {5}{-1+x}+\frac {x}{\log (x)}}}{-1+x}+2 e^{\frac {5}{-1+x}+\frac {x}{\log (x)}} x\right ) \, dx-\int \left (-\frac {e^{\frac {5}{-1+x}+\frac {x}{\log (x)}} x}{\log ^2(x)}+\frac {e^{\frac {5}{-1+x}+\frac {x}{\log (x)}} x^2}{\log ^2(x)}\right ) \, dx+\int \left (-\frac {e^{\frac {5}{-1+x}+\frac {x}{\log (x)}} x}{\log (x)}+\frac {e^{\frac {5}{-1+x}+\frac {x}{\log (x)}} x^2}{\log (x)}\right ) \, dx\\ &=-2 x^2+2 x^3+2 \int e^{\frac {5}{-1+x}+\frac {x}{\log (x)}} x \, dx-5 \int \frac {e^{\frac {5}{-1+x}+\frac {x}{\log (x)}}}{-1+x} \, dx-6 \int e^{\frac {5}{-1+x}+\frac {x}{\log (x)}} \, dx+\int \frac {e^{\frac {5}{-1+x}+\frac {x}{\log (x)}} x}{\log ^2(x)} \, dx-\int \frac {e^{\frac {5}{-1+x}+\frac {x}{\log (x)}} x^2}{\log ^2(x)} \, dx-\int \frac {e^{\frac {5}{-1+x}+\frac {x}{\log (x)}} x}{\log (x)} \, dx+\int \frac {e^{\frac {5}{-1+x}+\frac {x}{\log (x)}} x^2}{\log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 2.07, size = 25, normalized size = 0.89 \begin {gather*} (-1+x) x \left (e^{\frac {5}{-1+x}+\frac {x}{\log (x)}}+2 x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 41, normalized size = 1.46 \begin {gather*} 2 \, x^{3} - 2 \, x^{2} + {\left (x^{2} - x\right )} e^{\left (\frac {x^{2} - x + 5 \, \log \relax (x)}{{\left (x - 1\right )} \log \relax (x)}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 42, normalized size = 1.50
method | result | size |
risch | \(2 x^{3}-2 x^{2}+\left (x^{2}-x \right ) {\mathrm e}^{\frac {5 \ln \relax (x )+x^{2}-x}{\left (x -1\right ) \ln \relax (x )}}\) | \(42\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.17, size = 34, normalized size = 1.21 \begin {gather*} 2 \, x^{3} - 2 \, x^{2} + {\left (x^{2} - x\right )} e^{\left (\frac {x}{\log \relax (x)} + \frac {5}{x - 1}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.38, size = 55, normalized size = 1.96 \begin {gather*} x\,\left (2\,x+\frac {{\mathrm {e}}^{\frac {x}{\ln \relax (x)-x\,\ln \relax (x)}-\frac {x^2}{\ln \relax (x)-x\,\ln \relax (x)}}}{x^{\frac {5}{\ln \relax (x)-x\,\ln \relax (x)}}}\right )\,\left (x-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 13.71, size = 32, normalized size = 1.14 \begin {gather*} 2 x^{3} - 2 x^{2} + \left (x^{2} - x\right ) e^{\frac {x^{2} - x + 5 \log {\relax (x )}}{\left (x - 1\right ) \log {\relax (x )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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