Optimal. Leaf size=19 \[ e^{\frac {1}{4} \left (e^x+4 x\right )}-x \log (x) \]
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Rubi [A]
time = 0.03, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 3, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {12, 6838, 2332}
\begin {gather*} e^{\frac {1}{4} \left (4 x+e^x\right )}-x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2332
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \left (-4+e^{\frac {1}{4} \left (e^x+4 x\right )} \left (4+e^x\right )-4 \log (x)\right ) \, dx\\ &=-x+\frac {1}{4} \int e^{\frac {1}{4} \left (e^x+4 x\right )} \left (4+e^x\right ) \, dx-\int \log (x) \, dx\\ &=e^{\frac {1}{4} \left (e^x+4 x\right )}-x \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 17, normalized size = 0.89 \begin {gather*} e^{\frac {e^x}{4}+x}-x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 15, normalized size = 0.79
method | result | size |
norman | \({\mathrm e}^{x +\frac {{\mathrm e}^{x}}{4}}-x \ln \left (x \right )\) | \(14\) |
risch | \({\mathrm e}^{x +\frac {{\mathrm e}^{x}}{4}}-x \ln \left (x \right )\) | \(14\) |
default | \({\mathrm e}^{x} {\mathrm e}^{\frac {{\mathrm e}^{x}}{4}}-x \ln \left (x \right )\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 13, normalized size = 0.68 \begin {gather*} -x \log \left (x\right ) + e^{\left (x + \frac {1}{4} \, 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 = 13, normalized size = 0.68 \begin {gather*} -x \log \left (x\right ) + e^{\left (x + \frac {1}{4} \, e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 12, normalized size = 0.63 \begin {gather*} - x \log {\left (x \right )} + e^{x + \frac {e^{x}}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 13, normalized size = 0.68 \begin {gather*} -x \log \left (x\right ) + e^{\left (x + \frac {1}{4} \, e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.14, size = 13, normalized size = 0.68 \begin {gather*} {\mathrm {e}}^{x+\frac {{\mathrm {e}}^x}{4}}-x\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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