Optimal. Leaf size=19 \[ -e^{e^x+x} x+x^2+\log (3+\log (4)) \]
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Rubi [F] time = 0.11, 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 {2 x^2+e^{e^x+x} x \left (-1-x-e^x 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 x-e^{e^x+2 x} x-e^{e^x+x} (1+x)\right ) \, dx\\ &=x^2-\int e^{e^x+2 x} x \, dx-\int e^{e^x+x} (1+x) \, dx\\ &=x^2-\int e^{e^x+2 x} x \, dx-\int \left (e^{e^x+x}+e^{e^x+x} x\right ) \, dx\\ &=x^2-\int e^{e^x+x} \, dx-\int e^{e^x+x} x \, dx-\int e^{e^x+2 x} x \, dx\\ &=x^2-\int e^{e^x+x} x \, dx-\int e^{e^x+2 x} x \, dx-\operatorname {Subst}\left (\int e^x \, dx,x,e^x\right )\\ &=-e^{e^x}+x^2-\int e^{e^x+x} x \, dx-\int e^{e^x+2 x} x \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 13, normalized size = 0.68 \begin {gather*} x \left (-e^{e^x+x}+x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 13, normalized size = 0.68 \begin {gather*} x^{2} - e^{\left (x + e^{x} + \log \relax (x)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.26, size = 12, normalized size = 0.63 \begin {gather*} x^{2} - x e^{\left (x + e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 13, normalized size = 0.68
method | result | size |
risch | \(x^{2}-x \,{\mathrm e}^{{\mathrm e}^{x}+x}\) | \(13\) |
norman | \(x^{2}-{\mathrm e}^{x +\ln \relax (x )+{\mathrm e}^{x}}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 20, normalized size = 1.05 \begin {gather*} x^{2} - {\left (x e^{x} - 1\right )} e^{\left (e^{x}\right )} - e^{\left (e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.98, size = 11, normalized size = 0.58 \begin {gather*} x\,\left (x-{\mathrm {e}}^{x+{\mathrm {e}}^x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 10, normalized size = 0.53 \begin {gather*} x^{2} - x e^{x + e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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