Optimal. Leaf size=21 \[ 2 \left (-2+e^3+x-\log \left (5+e^{-3+x}-2 x\right )\right ) \]
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Rubi [F] time = 0.18, 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 {14-4 x}{5+e^{-3+x}-2 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 {14 e^3}{-5 e^3-e^x+2 e^3 x}+\frac {4 e^3 x}{-5 e^3-e^x+2 e^3 x}\right ) \, dx\\ &=\left (4 e^3\right ) \int \frac {x}{-5 e^3-e^x+2 e^3 x} \, dx-\left (14 e^3\right ) \int \frac {1}{-5 e^3-e^x+2 e^3 x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.08, size = 22, normalized size = 1.05 \begin {gather*} 2 x-2 \log \left (5 e^3+e^x-2 e^3 x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 16, normalized size = 0.76 \begin {gather*} 2 \, x - 2 \, \log \left (-2 \, x + e^{\left (x - 3\right )} + 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 21, normalized size = 1.00 \begin {gather*} 2 \, x - 2 \, \log \left (2 \, x e^{3} - 5 \, e^{3} - e^{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 18, normalized size = 0.86
method | result | size |
risch | \(-6+2 x -2 \ln \left ({\mathrm e}^{x -3}-2 x +5\right )\) | \(18\) |
norman | \(2 x -2 \ln \left (-{\mathrm e}^{x -3}+2 x -5\right )\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 19, normalized size = 0.90 \begin {gather*} 2 \, x - 2 \, \log \left (-2 \, x e^{3} + 5 \, e^{3} + e^{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.74, size = 18, normalized size = 0.86 \begin {gather*} 2\,x-2\,\ln \left (2\,x-{\mathrm {e}}^{x-3}-5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 15, normalized size = 0.71 \begin {gather*} 2 x - 2 \log {\left (- 2 x + e^{x - 3} + 5 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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