Optimal. Leaf size=18 \[ \frac {5}{4} e^{-3+x} (-4-x+2 \log (4)) \]
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Rubi [A]
time = 0.02, antiderivative size = 26, normalized size of antiderivative = 1.44, number of steps
used = 3, number of rules used = 3, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 2207, 2225}
\begin {gather*} \frac {5 e^{x-3}}{4}-\frac {5}{4} e^{x-3} (x+5-\log (16)) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2207
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int e^{-3+x} (-25-5 x+10 \log (4)) \, dx\\ &=-\frac {5}{4} e^{-3+x} (5+x-\log (16))+\frac {5}{4} \int e^{-3+x} \, dx\\ &=\frac {5 e^{-3+x}}{4}-\frac {5}{4} e^{-3+x} (5+x-\log (16))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 16, normalized size = 0.89 \begin {gather*} -\frac {5}{4} e^{-3+x} (4+x-2 \log (4)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.52, size = 39, normalized size = 2.17
method | result | size |
risch | \(\frac {\left (20 \ln \left (2\right )-20-5 x \right ) {\mathrm e}^{x -3}}{4}\) | \(16\) |
norman | \(\left (-\frac {5 x}{4}-5+5 \ln \left (2\right )\right ) {\mathrm e}^{x -3}\) | \(19\) |
gosper | \(\frac {5 \left (4 \ln \left (2\right )-4-x \right ) {\mathrm e}^{x -3}}{4}\) | \(20\) |
derivativedivides | \(\frac {5 \,{\mathrm e}^{x -3} \left (3-x \right )}{4}-\frac {35 \,{\mathrm e}^{x -3}}{4}+5 \,{\mathrm e}^{x -3} \ln \left (2\right )\) | \(39\) |
default | \(\frac {5 \,{\mathrm e}^{x -3} \left (3-x \right )}{4}-\frac {35 \,{\mathrm e}^{x -3}}{4}+5 \,{\mathrm e}^{x -3} \ln \left (2\right )\) | \(39\) |
meijerg | \(\frac {25 \,{\mathrm e}^{x -{\mathrm e}^{-3} x} \left (1-{\mathrm e}^{{\mathrm e}^{-3} x}\right )}{4}-5 \,{\mathrm e}^{x -{\mathrm e}^{-3} x} \ln \left (2\right ) \left (1-{\mathrm e}^{{\mathrm e}^{-3} x}\right )-\frac {5 \,{\mathrm e}^{x -{\mathrm e}^{-3} x +3} \left (1-\frac {\left (2-2 \,{\mathrm e}^{-3} x \right ) {\mathrm e}^{{\mathrm e}^{-3} x}}{2}\right )}{4}\) | \(69\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 24, normalized size = 1.33 \begin {gather*} -\frac {5}{4} \, {\left (x - 1\right )} e^{\left (x - 3\right )} + 5 \, e^{\left (x - 3\right )} \log \left (2\right ) - \frac {25}{4} \, e^{\left (x - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 13, normalized size = 0.72 \begin {gather*} -\frac {5}{4} \, {\left (x - 4 \, \log \left (2\right ) + 4\right )} e^{\left (x - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 15, normalized size = 0.83 \begin {gather*} \frac {\left (- 5 x - 20 + 20 \log {\left (2 \right )}\right ) e^{x - 3}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 13, normalized size = 0.72 \begin {gather*} -\frac {5}{4} \, {\left (x - 4 \, \log \left (2\right ) + 4\right )} e^{\left (x - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.97, size = 15, normalized size = 0.83 \begin {gather*} -{\mathrm {e}}^{-3}\,{\mathrm {e}}^x\,\left (\frac {5\,x}{4}-5\,\ln \left (2\right )+5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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