Optimal. Leaf size=25 \[ \log \left (-1+e^{\left (e^x+x^2\right )^{\frac {x+\log (x)}{x}}}+\log \left (x^2\right )\right ) \]
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Rubi [F] time = 180.00, 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*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
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Rubi steps
Aborted
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Mathematica [A] time = 0.44, size = 25, normalized size = 1.00 \begin {gather*} \log \left (-1+e^{\left (e^x+x^2\right )^{\frac {x+\log (x)}{x}}}+\log \left (x^2\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 23, normalized size = 0.92 \begin {gather*} \log \left (e^{\left ({\left (x^{2} + e^{x}\right )}^{\frac {x + \log \relax (x)}{x}}\right )} + 2 \, \log \relax (x) - 1\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^{3} + {\left (2 \, x^{3} + x^{2} e^{x} + {\left (x^{2} - {\left (x^{2} + e^{x}\right )} \log \relax (x) + e^{x}\right )} \log \left (x^{2} + e^{x}\right ) + {\left (2 \, x^{2} + x e^{x}\right )} \log \relax (x)\right )} {\left (x^{2} + e^{x}\right )}^{\frac {x + \log \relax (x)}{x}} e^{\left ({\left (x^{2} + e^{x}\right )}^{\frac {x + \log \relax (x)}{x}}\right )} + 2 \, x e^{x}}{x^{4} + x^{2} e^{x} - {\left (x^{4} + x^{2} e^{x}\right )} e^{\left ({\left (x^{2} + e^{x}\right )}^{\frac {x + \log \relax (x)}{x}}\right )} - {\left (x^{4} + x^{2} e^{x}\right )} \log \left (x^{2}\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.26, size = 74, normalized size = 2.96
method | result | size |
risch | \(\ln \left ({\mathrm e}^{\left (x^{2}+{\mathrm e}^{x}\right )^{\frac {x +\ln \relax (x )}{x}}}-\frac {i \left (\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}+4 i \ln \relax (x )-2 i\right )}{2}\right )\) | \(74\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.15, size = 83, normalized size = 3.32 \begin {gather*} x^{2} e^{\left (\frac {\log \left (x^{2} + e^{x}\right ) \log \relax (x)}{x}\right )} + \log \left ({\left (e^{\left (x^{2} e^{\left (\frac {\log \left (x^{2} + e^{x}\right ) \log \relax (x)}{x}\right )} + e^{\left (x + \frac {\log \left (x^{2} + e^{x}\right ) \log \relax (x)}{x}\right )}\right )} + 2 \, \log \relax (x) - 1\right )} e^{\left (-x^{2} e^{\left (\frac {\log \left (x^{2} + e^{x}\right ) \log \relax (x)}{x}\right )}\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.44, size = 42, normalized size = 1.68 \begin {gather*} \ln \left (\ln \left (x^2\right )+{\mathrm {e}}^{x^{\frac {\ln \left ({\mathrm {e}}^x+x^2\right )}{x}}\,x^2+x^{\frac {\ln \left ({\mathrm {e}}^x+x^2\right )}{x}}\,{\mathrm {e}}^x}-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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