Optimal. Leaf size=22 \[ 5 e^{2+e^x-\frac {x}{3}}-e^{-7+x} \]
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Rubi [A]
time = 0.06, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps
used = 5, number of rules used = 4, integrand size = 43, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.093, Rules used = {12, 2320, 14,
2326} \begin {gather*} 5 e^{-\frac {x}{3}+e^x+2}-e^{x-7} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2320
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int e^{\frac {6-x}{3}} \left (-3 e^{-7+\frac {1}{3} (-6+x)+x}+e^{e^x} \left (-5+15 e^x\right )\right ) \, dx\\ &=\text {Subst}\left (\int \frac {-\frac {3 x^3}{e^7}+\frac {5 e^{2+x^3} \left (-1+3 x^3\right )}{x}}{x} \, dx,x,e^{x/3}\right )\\ &=\text {Subst}\left (\int \left (-\frac {3 x^2}{e^7}+\frac {5 e^{2+x^3} \left (-1+3 x^3\right )}{x^2}\right ) \, dx,x,e^{x/3}\right )\\ &=-e^{-7+x}+5 \text {Subst}\left (\int \frac {e^{2+x^3} \left (-1+3 x^3\right )}{x^2} \, dx,x,e^{x/3}\right )\\ &=5 e^{2+e^x-\frac {x}{3}}-e^{-7+x}\\ \end {aligned} \end {gather*}
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Mathematica [C] Result contains higher order function than in optimal. Order 4 vs. order 3 in
optimal.
time = 0.04, size = 68, normalized size = 3.09 \begin {gather*} -e^{-7+x}+\frac {5}{3} e^{2-\frac {x}{3}} \sqrt [3]{-e^x} \Gamma \left (-\frac {1}{3},-e^x\right )+5 e^{2-\frac {x}{3}} \sqrt [3]{-e^x} \Gamma \left (\frac {2}{3},-e^x\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.16, size = 18, normalized size = 0.82
method | result | size |
risch | \(-{\mathrm e}^{x -7}+5 \,{\mathrm e}^{-\frac {x}{3}+2+{\mathrm e}^{x}}\) | \(18\) |
norman | \(\left (5 \,{\mathrm e}^{2} {\mathrm e}^{{\mathrm e}^{x}}-{\mathrm e}^{-7} {\mathrm e}^{\frac {4 x}{3}}\right ) {\mathrm e}^{-\frac {x}{3}}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 17, normalized size = 0.77 \begin {gather*} -e^{\left (x - 7\right )} + 5 \, e^{\left (-\frac {1}{3} \, x + e^{x} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 17, normalized size = 0.77 \begin {gather*} {\left (5 \, e^{\left (-\frac {4}{3} \, x + e^{x} + 9\right )} - 1\right )} e^{\left (x - 7\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.17, size = 22, normalized size = 1.00 \begin {gather*} - \frac {e^{x}}{e^{7}} + \frac {5 e^{2} e^{e^{x}}}{\sqrt [3]{e^{x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 23, normalized size = 1.05 \begin {gather*} -{\left (e^{\left (2 \, x\right )} - 5 \, e^{\left (\frac {2}{3} \, x + e^{x} + 9\right )}\right )} e^{\left (-x - 7\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.17, size = 22, normalized size = 1.00 \begin {gather*} -\frac {{\mathrm {e}}^{-\frac {x}{3}}\,\left (3\,{\mathrm {e}}^{\frac {4\,x}{3}-7}-15\,{\mathrm {e}}^{{\mathrm {e}}^x+2}\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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