Optimal. Leaf size=16 \[ \frac {3}{2} \left (-\frac {3}{16}-e^{-5+x} x\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.38, number of steps used = 3, number of rules used = 3, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.214, Rules used = {12, 2176, 2194} \begin {gather*} \frac {3 e^{x-5}}{2}-\frac {3}{2} e^{x-5} (x+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2176
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int e^{-5+x} (-3-3 x) \, dx\\ &=-\frac {3}{2} e^{-5+x} (1+x)+\frac {3}{2} \int e^{-5+x} \, dx\\ &=\frac {3 e^{-5+x}}{2}-\frac {3}{2} e^{-5+x} (1+x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 10, normalized size = 0.62 \begin {gather*} -\frac {3}{2} e^{-5+x} x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 8, normalized size = 0.50 \begin {gather*} -\frac {3}{2} \, e^{\left (x + \log \relax (x) - 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.50, size = 7, normalized size = 0.44 \begin {gather*} -\frac {3}{2} \, x e^{\left (x - 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 8, normalized size = 0.50
method | result | size |
risch | \(-\frac {3 x \,{\mathrm e}^{x -5}}{2}\) | \(8\) |
gosper | \(-\frac {3 \,{\mathrm e}^{\ln \relax (x )+x -5}}{2}\) | \(9\) |
norman | \(-\frac {3 \,{\mathrm e}^{\ln \relax (x )+x -5}}{2}\) | \(9\) |
default | \(-\frac {3 \,{\mathrm e}^{x -5} \left (x -5\right )}{2}-\frac {15 \,{\mathrm e}^{x -5}}{2}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 16, normalized size = 1.00 \begin {gather*} -\frac {3}{2} \, {\left (x - 1\right )} e^{\left (x - 5\right )} - \frac {3}{2} \, e^{\left (x - 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.44, size = 7, normalized size = 0.44 \begin {gather*} -\frac {3\,x\,{\mathrm {e}}^{-5}\,{\mathrm {e}}^x}{2} \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 = 0.62 \begin {gather*} - \frac {3 x e^{x - 5}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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