Optimal. Leaf size=11 \[ e^{x^x} \left (x^x-1\right ) \]
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Rubi [F] time = 0.15, 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 = {} \[ \int e^{x^x} x^{2 x} (1+\log (x)) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int e^{x^x} x^{2 x} (1+\log (x)) \, dx &=\int \left (e^{x^x} x^{2 x}+e^{x^x} x^{2 x} \log (x)\right ) \, dx\\ &=\int e^{x^x} x^{2 x} \, dx+\int e^{x^x} x^{2 x} \log (x) \, dx\\ &=\log (x) \int e^{x^x} x^{2 x} \, dx+\int e^{x^x} x^{2 x} \, dx-\int \frac {\int e^{x^x} x^{2 x} \, dx}{x} \, dx\\ \end {align*}
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Mathematica [A] time = 0.04, size = 11, normalized size = 1.00 \[ e^{x^x} \left (x^x-1\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 10, normalized size = 0.91 \[ {\left (x^{x} - 1\right )} e^{\left (x^{x}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 10, normalized size = 0.91 \[ {\left (x^{x} - 1\right )} e^{\left (x^{x}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.05, size = 22, normalized size = 2.00 \[ {\mathrm e}^{x \ln \relax (x )} {\mathrm e}^{{\mathrm e}^{x \ln \relax (x )}}-{\mathrm e}^{{\mathrm e}^{x \ln \relax (x )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.30, size = 10, normalized size = 0.91 \[ {\left (x^{x} - 1\right )} e^{\left (x^{x}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.59, size = 10, normalized size = 0.91 \[ {\mathrm {e}}^{x^x}\,\left (x^x-1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.45, size = 8, normalized size = 0.73 \[ \left (x^{x} - 1\right ) e^{x^{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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