Optimal. Leaf size=28 \[ \log \left (e^{1-x} x+e^{5-x} \left (5-e^4+\log (x)\right )\right ) \]
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Rubi [A]
time = 0.49, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 3, integrand size = 89, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {6820, 6874,
6816} \begin {gather*} \log \left (-x-e^4 \log (x)-e^4 \left (5-e^4\right )\right )-x \end {gather*}
Antiderivative was successfully verified.
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Rule 6816
Rule 6820
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^4+\left (1+e^4 \left (-5+e^4\right )\right ) x-x^2-e^4 x \log (x)}{x \left (5 e^4 \left (1-\frac {e^4}{5}\right )+x+e^4 \log (x)\right )} \, dx\\ &=\int \left (-1+\frac {e^4+x}{x \left (5 e^4 \left (1-\frac {e^4}{5}\right )+x+e^4 \log (x)\right )}\right ) \, dx\\ &=-x+\int \frac {e^4+x}{x \left (5 e^4 \left (1-\frac {e^4}{5}\right )+x+e^4 \log (x)\right )} \, dx\\ &=-x+\log \left (-e^4 \left (5-e^4\right )-x-e^4 \log (x)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.09, size = 24, normalized size = 0.86 \begin {gather*} -x+\log \left (-5 e^4+e^8-x-e^4 \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 22, normalized size = 0.79
method | result | size |
risch | \(-x +\ln \left (\ln \left (x \right )+\left ({\mathrm e}^{-8} x +5 \,{\mathrm e}^{-4}-1\right ) {\mathrm e}^{4}\right )\) | \(22\) |
norman | \(-x +\ln \left ({\mathrm e}^{8}-{\mathrm e}^{4} \ln \left (x \right )-5 \,{\mathrm e}^{4}-x \right )\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 23, normalized size = 0.82 \begin {gather*} -x + \log \left ({\left (e^{4} \log \left (x\right ) + x - e^{8} + 5 \, e^{4}\right )} e^{\left (-4\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 20, normalized size = 0.71 \begin {gather*} -x + \log \left (e^{4} \log \left (x\right ) + x - e^{8} + 5 \, e^{4}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.12, size = 19, normalized size = 0.68 \begin {gather*} - x + \log {\left (\frac {x - e^{8} + 5 e^{4}}{e^{4}} + \log {\left (x \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 21, normalized size = 0.75 \begin {gather*} -x + \log \left (-e^{4} \log \left (x\right ) - x + e^{8} - 5 \, e^{4}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.90, size = 17, normalized size = 0.61 \begin {gather*} \ln \left (\ln \left (x\right )-{\mathrm {e}}^4+x\,{\mathrm {e}}^{-4}+5\right )-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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