Optimal. Leaf size=23 \[ e^{e^x x} \left (5+e^x+x\right )+x^2 \log ^2(7) \]
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Rubi [F] time = 1.12, 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 {e^{e^x x} \left (5+e^x+x\right ) \left (1+e^{2 x} (1+x)+e^x \left (6+6 x+x^2\right )\right )+2 e^x x \log ^2(7)+\left (10 x+2 x^2\right ) \log ^2(7)}{5+e^x+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 (e^{e^x x} \left (1+6 e^x+e^{2 x}+6 e^x x+e^{2 x} x+e^x x^2\right )+2 x \log ^2(7)\right ) \, dx\\ &=x^2 \log ^2(7)+\int e^{e^x x} \left (1+6 e^x+e^{2 x}+6 e^x x+e^{2 x} x+e^x x^2\right ) \, dx\\ &=x^2 \log ^2(7)+\int e^{e^x x} \left (1+e^{2 x} (1+x)+e^x \left (6+6 x+x^2\right )\right ) \, dx\\ &=x^2 \log ^2(7)+\int \left (e^{e^x x}+e^{2 x+e^x x} (1+x)+e^{x+e^x x} \left (6+6 x+x^2\right )\right ) \, dx\\ &=x^2 \log ^2(7)+\int e^{e^x x} \, dx+\int e^{2 x+e^x x} (1+x) \, dx+\int e^{x+e^x x} \left (6+6 x+x^2\right ) \, dx\\ &=x^2 \log ^2(7)+\int e^{e^x x} \, dx+\int \left (e^{2 x+e^x x}+e^{2 x+e^x x} x\right ) \, dx+\int \left (6 e^{x+e^x x}+6 e^{x+e^x x} x+e^{x+e^x x} x^2\right ) \, dx\\ &=x^2 \log ^2(7)+6 \int e^{x+e^x x} \, dx+6 \int e^{x+e^x x} x \, dx+\int e^{e^x x} \, dx+\int e^{2 x+e^x x} \, dx+\int e^{2 x+e^x x} x \, dx+\int e^{x+e^x x} x^2 \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 29, normalized size = 1.26 \begin {gather*} e^{x+e^x x}+e^{e^x x} (5+x)+x^2 \log ^2(7) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.05, size = 21, normalized size = 0.91 \begin {gather*} x^{2} \log \relax (7)^{2} + e^{\left (x e^{x} + \log \left (x + e^{x} + 5\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 \, x e^{x} \log \relax (7)^{2} + 2 \, {\left (x^{2} + 5 \, x\right )} \log \relax (7)^{2} + {\left ({\left (x + 1\right )} e^{\left (2 \, x\right )} + {\left (x^{2} + 6 \, x + 6\right )} e^{x} + 1\right )} e^{\left (x e^{x} + \log \left (x + e^{x} + 5\right )\right )}}{x + e^{x} + 5}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 21, normalized size = 0.91
method | result | size |
risch | \(\left ({\mathrm e}^{x}+5+x \right ) {\mathrm e}^{{\mathrm e}^{x} x}+x^{2} \ln \relax (7)^{2}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 20, normalized size = 0.87 \begin {gather*} x^{2} \log \relax (7)^{2} + {\left (x + e^{x} + 5\right )} e^{\left (x e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.50, size = 30, normalized size = 1.30 \begin {gather*} 5\,{\mathrm {e}}^{x\,{\mathrm {e}}^x}+{\mathrm {e}}^{x+x\,{\mathrm {e}}^x}+x^2\,{\ln \relax (7)}^2+x\,{\mathrm {e}}^{x\,{\mathrm {e}}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.24, size = 20, normalized size = 0.87 \begin {gather*} x^{2} \log {\relax (7 )}^{2} + \left (x + e^{x} + 5\right ) e^{x e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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