Optimal. Leaf size=26 \[ x+\log (6)-\log \left (\frac {1}{2} e^{4+e^{1-\frac {x}{5}} x}\right ) \]
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Rubi [A]
time = 0.07, antiderivative size = 28, normalized size of antiderivative = 1.08, number of steps
used = 5, number of rules used = 4, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.138, Rules used = {12, 6820, 2207,
2225} \begin {gather*} e^{1-\frac {x}{5}} (5-x)-5 e^{1-\frac {x}{5}}+x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2207
Rule 2225
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int e^{\frac {5-x}{5}} \left (-5+5 e^{\frac {1}{5} (-5+x)}+x\right ) \, dx\\ &=\frac {1}{5} \int \left (5+e^{1-\frac {x}{5}} (-5+x)\right ) \, dx\\ &=x+\frac {1}{5} \int e^{1-\frac {x}{5}} (-5+x) \, dx\\ &=e^{1-\frac {x}{5}} (5-x)+x+\int e^{1-\frac {x}{5}} \, dx\\ &=-5 e^{1-\frac {x}{5}}+e^{1-\frac {x}{5}} (5-x)+x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.08, size = 14, normalized size = 0.54 \begin {gather*} x-e^{1-\frac {x}{5}} x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.41, size = 29, normalized size = 1.12
method | result | size |
risch | \(x -x \,{\mathrm e}^{1-\frac {x}{5}}\) | \(12\) |
norman | \(\left (x \,{\mathrm e}^{\frac {x}{5}-1}-x \right ) {\mathrm e}^{1-\frac {x}{5}}\) | \(22\) |
derivativedivides | \(x -5-5 \,{\mathrm e}^{1-\frac {x}{5}} \left (\frac {x}{5}-1\right )-5 \,{\mathrm e}^{1-\frac {x}{5}}\) | \(29\) |
default | \(x -5-5 \,{\mathrm e}^{1-\frac {x}{5}} \left (\frac {x}{5}-1\right )-5 \,{\mathrm e}^{1-\frac {x}{5}}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 25, normalized size = 0.96 \begin {gather*} -{\left (x e + 5 \, e\right )} e^{\left (-\frac {1}{5} \, x\right )} + x + 5 \, e^{\left (-\frac {1}{5} \, x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 19, normalized size = 0.73 \begin {gather*} {\left (x e^{\left (\frac {1}{5} \, x - 1\right )} - x\right )} e^{\left (-\frac {1}{5} \, x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 8, normalized size = 0.31 \begin {gather*} - x e^{1 - \frac {x}{5}} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 12, normalized size = 0.46 \begin {gather*} -x e^{\left (-\frac {1}{5} \, x + 1\right )} + x - 5 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 11, normalized size = 0.42 \begin {gather*} -x\,\left ({\mathrm {e}}^{1-\frac {x}{5}}-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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