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 = 0.79, 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 = 0.03, 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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Maple [A]
time = 0.33, size = 21, normalized size = 0.91
method | result | size |
risch | \(\left ({\mathrm e}^{x}+5+x \right ) {\mathrm e}^{{\mathrm e}^{x} x}+x^{2} \ln \left (7\right )^{2}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.64, size = 20, normalized size = 0.87 \begin {gather*} x^{2} \log \left (7\right )^{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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Fricas [A]
time = 0.34, size = 21, normalized size = 0.91 \begin {gather*} x^{2} \log \left (7\right )^{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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Sympy [A]
time = 0.11, size = 20, normalized size = 0.87 \begin {gather*} x^{2} \log {\left (7 \right )}^{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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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \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 \left (7\right )}^2+x\,{\mathrm {e}}^{x\,{\mathrm {e}}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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