Optimal. Leaf size=17 \[ -x+\log \left (-4+5 e^x-x+\log (x)\right ) \]
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Rubi [F] time = 0.45, 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*} \int \frac {1+3 x+x^2-x \log (x)}{-4 x+5 e^x x-x^2+x \log (x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {1}{x \left (4-5 e^x+x-\log (x)\right )}-\frac {x}{4-5 e^x+x-\log (x)}+\frac {3}{-4+5 e^x-x+\log (x)}-\frac {\log (x)}{-4+5 e^x-x+\log (x)}\right ) \, dx\\ &=3 \int \frac {1}{-4+5 e^x-x+\log (x)} \, dx-\int \frac {1}{x \left (4-5 e^x+x-\log (x)\right )} \, dx-\int \frac {x}{4-5 e^x+x-\log (x)} \, dx-\int \frac {\log (x)}{-4+5 e^x-x+\log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.14, size = 17, normalized size = 1.00 \begin {gather*} -x+\log \left (4-5 e^x+x-\log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.50, size = 16, normalized size = 0.94 \begin {gather*} -x + \log \left (-x + 5 \, e^{x} + \log \relax (x) - 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.39, size = 16, normalized size = 0.94 \begin {gather*} -x + \log \left (x - 5 \, e^{x} - \log \relax (x) + 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 17, normalized size = 1.00
method | result | size |
norman | \(-x +\ln \left (x -5 \,{\mathrm e}^{x}-\ln \relax (x )+4\right )\) | \(17\) |
risch | \(\ln \left (\ln \relax (x )+5 \,{\mathrm e}^{x}-4-x \right )-x\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 16, normalized size = 0.94 \begin {gather*} -x + \log \left (-\frac {1}{5} \, x + e^{x} + \frac {1}{5} \, \log \relax (x) - \frac {4}{5}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.07, size = 16, normalized size = 0.94 \begin {gather*} \ln \left (x-5\,{\mathrm {e}}^x-\ln \relax (x)+4\right )-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.35, size = 17, normalized size = 1.00 \begin {gather*} - x + \log {\left (- \frac {x}{5} + e^{x} + \frac {\log {\relax (x )}}{5} - \frac {4}{5} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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