Optimal. Leaf size=26 \[ -1-e^x+\frac {4}{5} \left (\frac {e^3}{3}-x\right )+\log (2 x) \]
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Rubi [A] time = 0.01, antiderivative size = 13, normalized size of antiderivative = 0.50, number of steps used = 6, number of rules used = 4, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 14, 2194, 43} \begin {gather*} -\frac {4 x}{5}-e^x+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 43
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {5-4 x-5 e^x x}{x} \, dx\\ &=\frac {1}{5} \int \left (-5 e^x+\frac {5-4 x}{x}\right ) \, dx\\ &=\frac {1}{5} \int \frac {5-4 x}{x} \, dx-\int e^x \, dx\\ &=-e^x+\frac {1}{5} \int \left (-4+\frac {5}{x}\right ) \, dx\\ &=-e^x-\frac {4 x}{5}+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 13, normalized size = 0.50 \begin {gather*} -e^x-\frac {4 x}{5}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 10, normalized size = 0.38 \begin {gather*} -\frac {4}{5} \, x - e^{x} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 10, normalized size = 0.38 \begin {gather*} -\frac {4}{5} \, x - e^{x} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 11, normalized size = 0.42
method | result | size |
default | \(-\frac {4 x}{5}+\ln \relax (x )-{\mathrm e}^{x}\) | \(11\) |
norman | \(-\frac {4 x}{5}+\ln \relax (x )-{\mathrm e}^{x}\) | \(11\) |
risch | \(-\frac {4 x}{5}+\ln \relax (x )-{\mathrm e}^{x}\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 10, normalized size = 0.38 \begin {gather*} -\frac {4}{5} \, x - e^{x} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.21, size = 10, normalized size = 0.38 \begin {gather*} \ln \relax (x)-{\mathrm {e}}^x-\frac {4\,x}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 10, normalized size = 0.38 \begin {gather*} - \frac {4 x}{5} - e^{x} + \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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