Optimal. Leaf size=28 \[ 3+2 e^{e^x-2 x+\left (-x-x^2+4 \log (x)\right )^2} \]
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Rubi [F] time = 10.65, 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 {\exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) \left (-20 x+2 e^x x-12 x^2+12 x^3+8 x^4+\left (64-16 x-32 x^2\right ) \log (x)\right )}{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 \exp \left (e^x-x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right )+\frac {4 \exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) \left (-5 x-3 x^2+3 x^3+2 x^4+16 \log (x)-4 x \log (x)-8 x^2 \log (x)\right )}{x}\right ) \, dx\\ &=2 \int \exp \left (e^x-x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) \, dx+4 \int \frac {\exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) \left (-5 x-3 x^2+3 x^3+2 x^4+16 \log (x)-4 x \log (x)-8 x^2 \log (x)\right )}{x} \, dx\\ &=2 \int \exp \left (e^x-x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) \, dx+4 \int \left (-5 \exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right )-3 \exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) x+3 \exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) x^2+2 \exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) x^3-\frac {4 \exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) \left (-4+x+2 x^2\right ) \log (x)}{x}\right ) \, dx\\ &=2 \int \exp \left (e^x-x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) \, dx+8 \int \exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) x^3 \, dx-12 \int \exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) x \, dx+12 \int \exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) x^2 \, dx-16 \int \frac {\exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) \left (-4+x+2 x^2\right ) \log (x)}{x} \, dx-20 \int \exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) \, dx\\ &=2 \int \exp \left (e^x-x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) \, dx+8 \int \exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) x^3 \, dx-12 \int \exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) x \, dx+12 \int \exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) x^2 \, dx-16 \int \left (\exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) \log (x)-\frac {4 \exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) \log (x)}{x}+2 \exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) x \log (x)\right ) \, dx-20 \int \exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) \, dx\\ &=2 \int \exp \left (e^x-x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) \, dx+8 \int \exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) x^3 \, dx-12 \int \exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) x \, dx+12 \int \exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) x^2 \, dx-16 \int \exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) \log (x) \, dx-20 \int \exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) \, dx-32 \int \exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) x \log (x) \, dx+64 \int \frac {\exp \left (e^x-2 x+x^2+2 x^3+x^4+\left (-8 x-8 x^2\right ) \log (x)+16 \log ^2(x)\right ) \log (x)}{x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 5.02, size = 36, normalized size = 1.29 \begin {gather*} 2 e^{e^x-2 x+x^2+2 x^3+x^4+16 \log ^2(x)} x^{-8 x (1+x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 35, normalized size = 1.25 \begin {gather*} 2 \, e^{\left (x^{4} + 2 \, x^{3} + x^{2} - 8 \, {\left (x^{2} + x\right )} \log \relax (x) + 16 \, \log \relax (x)^{2} - 2 \, x + e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 38, normalized size = 1.36 \begin {gather*} 2 \, e^{\left (x^{4} + 2 \, x^{3} - 8 \, x^{2} \log \relax (x) + x^{2} - 8 \, x \log \relax (x) + 16 \, \log \relax (x)^{2} - 2 \, x + e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 35, normalized size = 1.25
method | result | size |
risch | \(2 x^{-8 \left (x +1\right ) x} {\mathrm e}^{16 \ln \relax (x )^{2}+{\mathrm e}^{x}+x^{4}+2 x^{3}+x^{2}-2 x}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.60, size = 38, normalized size = 1.36 \begin {gather*} 2 \, e^{\left (x^{4} + 2 \, x^{3} - 8 \, x^{2} \log \relax (x) + x^{2} - 8 \, x \log \relax (x) + 16 \, \log \relax (x)^{2} - 2 \, x + e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.06, size = 43, normalized size = 1.54 \begin {gather*} \frac {2\,{\mathrm {e}}^{16\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^{2\,x^3}}{x^{8\,x^2+8\,x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.57, size = 41, normalized size = 1.46 \begin {gather*} 2 e^{x^{4} + 2 x^{3} + x^{2} - 2 x + \left (- 8 x^{2} - 8 x\right ) \log {\relax (x )} + e^{x} + 16 \log {\relax (x )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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