Optimal. Leaf size=23 \[ 1+2 x-e^{\left (4-e^{x^2}\right )^2} x+\log (x) \]
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Rubi [F] time = 0.28, 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 {1+2 x+e^{16-8 e^{x^2}+e^{2 x^2}} \left (-x+16 e^{x^2} x^3-4 e^{2 x^2} x^3\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 (16 e^{16-8 e^{x^2}+e^{2 x^2}+x^2} x^2-4 e^{16-8 e^{x^2}+e^{2 x^2}+2 x^2} x^2-\frac {-1-2 x+e^{\left (-4+e^{x^2}\right )^2} x}{x}\right ) \, dx\\ &=-\left (4 \int e^{16-8 e^{x^2}+e^{2 x^2}+2 x^2} x^2 \, dx\right )+16 \int e^{16-8 e^{x^2}+e^{2 x^2}+x^2} x^2 \, dx-\int \frac {-1-2 x+e^{\left (-4+e^{x^2}\right )^2} x}{x} \, dx\\ &=-\left (4 \int e^{16-8 e^{x^2}+e^{2 x^2}+2 x^2} x^2 \, dx\right )+16 \int e^{16-8 e^{x^2}+e^{2 x^2}+x^2} x^2 \, dx-\int \left (e^{\left (-4+e^{x^2}\right )^2}+\frac {-1-2 x}{x}\right ) \, dx\\ &=-\left (4 \int e^{16-8 e^{x^2}+e^{2 x^2}+2 x^2} x^2 \, dx\right )+16 \int e^{16-8 e^{x^2}+e^{2 x^2}+x^2} x^2 \, dx-\int e^{\left (-4+e^{x^2}\right )^2} \, dx-\int \frac {-1-2 x}{x} \, dx\\ &=-\left (4 \int e^{16-8 e^{x^2}+e^{2 x^2}+2 x^2} x^2 \, dx\right )+16 \int e^{16-8 e^{x^2}+e^{2 x^2}+x^2} x^2 \, dx-\int e^{\left (-4+e^{x^2}\right )^2} \, dx-\int \left (-2-\frac {1}{x}\right ) \, dx\\ &=2 x+\log (x)-4 \int e^{16-8 e^{x^2}+e^{2 x^2}+2 x^2} x^2 \, dx+16 \int e^{16-8 e^{x^2}+e^{2 x^2}+x^2} x^2 \, dx-\int e^{\left (-4+e^{x^2}\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.12, size = 19, normalized size = 0.83 \begin {gather*} -\left (\left (-2+e^{\left (-4+e^{x^2}\right )^2}\right ) x\right )+\log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 24, normalized size = 1.04 \begin {gather*} -x e^{\left (e^{\left (2 \, x^{2}\right )} - 8 \, e^{\left (x^{2}\right )} + 16\right )} + 2 \, x + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 24, normalized size = 1.04 \begin {gather*} -x e^{\left (e^{\left (2 \, x^{2}\right )} - 8 \, e^{\left (x^{2}\right )} + 16\right )} + 2 \, x + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 25, normalized size = 1.09
method | result | size |
norman | \(2 x -{\mathrm e}^{{\mathrm e}^{2 x^{2}}-8 \,{\mathrm e}^{x^{2}}+16} x +\ln \relax (x )\) | \(25\) |
risch | \(2 x -{\mathrm e}^{{\mathrm e}^{2 x^{2}}-8 \,{\mathrm e}^{x^{2}}+16} x +\ln \relax (x )\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 24, normalized size = 1.04 \begin {gather*} -x e^{\left (e^{\left (2 \, x^{2}\right )} - 8 \, e^{\left (x^{2}\right )} + 16\right )} + 2 \, x + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.13, size = 25, normalized size = 1.09 \begin {gather*} 2\,x+\ln \relax (x)-x\,{\mathrm {e}}^{{\mathrm {e}}^{2\,x^2}}\,{\mathrm {e}}^{-8\,{\mathrm {e}}^{x^2}}\,{\mathrm {e}}^{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 92.70, size = 24, normalized size = 1.04 \begin {gather*} - x e^{e^{2 x^{2}} - 8 e^{x^{2}} + 16} + 2 x + \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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