Optimal. Leaf size=22 \[ 3-\frac {2 \left (1+e^5\right ) \left (3+e^x\right )}{e^5}+e^x x \]
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Rubi [A]
time = 0.02, antiderivative size = 24, normalized size of antiderivative = 1.09, number of steps
used = 3, number of rules used = 3, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {2218, 2207,
2225} \begin {gather*} -e^{x-5} \left (-e^5 x+e^5+2\right )-e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 2207
Rule 2218
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int e^{-5+x} \left (-2-e^5+e^5 x\right ) \, dx\\ &=-e^{-5+x} \left (2+e^5-e^5 x\right )-e^5 \int e^{-5+x} \, dx\\ &=-e^x-e^{-5+x} \left (2+e^5-e^5 x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 12, normalized size = 0.55 \begin {gather*} e^x \left (-2-\frac {2}{e^5}+x\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.15, size = 29, normalized size = 1.32
method | result | size |
risch | \(\left (x \,{\mathrm e}^{5}-2 \,{\mathrm e}^{5}-2\right ) {\mathrm e}^{x -5}\) | \(16\) |
gosper | \({\mathrm e}^{x} \left (x \,{\mathrm e}^{5}-2 \,{\mathrm e}^{5}-2\right ) {\mathrm e}^{-5}\) | \(18\) |
norman | \({\mathrm e}^{x} x -2 \left ({\mathrm e}^{5}+1\right ) {\mathrm e}^{-5} {\mathrm e}^{x}\) | \(18\) |
meijerg | \(2 \,{\mathrm e}^{-5} \left (1-{\mathrm e}^{x}\right )+2-\frac {\left (-2 x +2\right ) {\mathrm e}^{x}}{2}-{\mathrm e}^{x}\) | \(26\) |
default | \({\mathrm e}^{-5} \left ({\mathrm e}^{5} \left ({\mathrm e}^{x} x -{\mathrm e}^{x}\right )-{\mathrm e}^{5} {\mathrm e}^{x}-2 \,{\mathrm e}^{x}\right )\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 17, normalized size = 0.77 \begin {gather*} {\left (x - 1\right )} e^{x} - 2 \, e^{\left (x - 5\right )} - e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 13, normalized size = 0.59 \begin {gather*} {\left ({\left (x - 2\right )} e^{5} - 2\right )} e^{\left (x - 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 17, normalized size = 0.77 \begin {gather*} \frac {\left (x e^{5} - 2 e^{5} - 2\right ) e^{x}}{e^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 13, normalized size = 0.59 \begin {gather*} {\left (x - 2\right )} e^{x} - 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 = 4.79, size = 17, normalized size = 0.77 \begin {gather*} -{\mathrm {e}}^{x-5}\,\left (2\,{\mathrm {e}}^5-x\,{\mathrm {e}}^5+2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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