Optimal. Leaf size=20 \[ e^{e^x+e^{\frac {1}{4}+2 x}}+x \log (x) \]
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Rubi [A]
time = 0.04, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 3, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {2320, 2268,
2332} \begin {gather*} e^{e^x+e^{2 x+\frac {1}{4}}}+x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2268
Rule 2320
Rule 2332
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x+\int e^{e^x+e^{\frac {1}{4} (1+8 x)}} \left (e^x+2 e^{\frac {1}{4} (1+8 x)}\right ) \, dx+\int \log (x) \, dx\\ &=x \log (x)+\text {Subst}\left (\int e^{x+\sqrt [4]{e} x^2} \left (1+2 \sqrt [4]{e} x\right ) \, dx,x,e^x\right )\\ &=e^{e^x+e^{\frac {1}{4}+2 x}}+x \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 20, normalized size = 1.00 \begin {gather*} e^{e^x+e^{\frac {1}{4}+2 x}}+x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 16, normalized size = 0.80
method | result | size |
default | \(x \ln \left (x \right )+{\mathrm e}^{{\mathrm e}^{2 x +\frac {1}{4}}+{\mathrm e}^{x}}\) | \(16\) |
risch | \(x \ln \left (x \right )+{\mathrm e}^{{\mathrm e}^{2 x +\frac {1}{4}}+{\mathrm e}^{x}}\) | \(16\) |
norman | \(x \ln \left (x \right )+{\mathrm e}^{{\mathrm e}^{\frac {1}{4}} {\mathrm e}^{2 x}+{\mathrm e}^{x}}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 15, normalized size = 0.75 \begin {gather*} x \log \left (x\right ) + e^{\left (e^{\left (2 \, x + \frac {1}{4}\right )} + e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 15, normalized size = 0.75 \begin {gather*} x \log \left (x\right ) + e^{\left (e^{\left (2 \, x + \frac {1}{4}\right )} + e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.13, size = 19, normalized size = 0.95 \begin {gather*} x \log {\left (x \right )} + e^{e^{\frac {1}{4}} e^{2 x} + e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 15, normalized size = 0.75 \begin {gather*} x \log \left (x\right ) + e^{\left (e^{\left (2 \, x + \frac {1}{4}\right )} + e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.40, size = 17, normalized size = 0.85 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^{{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{1/4}}+x\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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