Optimal. Leaf size=28 \[ e^{-e^x-5 \left (1+\frac {x}{9}\right )+x} \left (\frac {7}{2}-x\right )^2 \]
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Rubi [F] time = 1.00, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {1}{36} e^{\frac {1}{9} \left (-45-9 e^x+4 x\right )} \left (-56-40 x+16 x^2+e^x \left (-441+252 x-36 x^2\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{36} \int e^{\frac {1}{9} \left (-45-9 e^x+4 x\right )} \left (-56-40 x+16 x^2+e^x \left (-441+252 x-36 x^2\right )\right ) \, dx\\ &=\frac {1}{36} \int e^{\frac {1}{9} \left (-45-9 e^x+4 x\right )} (7-2 x) \left (-8-63 e^x-8 x+18 e^x x\right ) \, dx\\ &=\frac {1}{36} \int \left (-9 e^{x+\frac {1}{9} \left (-45-9 e^x+4 x\right )} (-7+2 x)^2+8 e^{\frac {1}{9} \left (-45-9 e^x+4 x\right )} \left (-7-5 x+2 x^2\right )\right ) \, dx\\ &=\frac {2}{9} \int e^{\frac {1}{9} \left (-45-9 e^x+4 x\right )} \left (-7-5 x+2 x^2\right ) \, dx-\frac {1}{4} \int e^{x+\frac {1}{9} \left (-45-9 e^x+4 x\right )} (-7+2 x)^2 \, dx\\ &=\frac {2}{9} \int \left (-7 e^{\frac {1}{9} \left (-45-9 e^x+4 x\right )}-5 e^{\frac {1}{9} \left (-45-9 e^x+4 x\right )} x+2 e^{\frac {1}{9} \left (-45-9 e^x+4 x\right )} x^2\right ) \, dx-\frac {1}{4} \int e^{\frac {1}{9} \left (-45-9 e^x+13 x\right )} (7-2 x)^2 \, dx\\ &=-\left (\frac {1}{4} \int \left (49 e^{\frac {1}{9} \left (-45-9 e^x+13 x\right )}-28 e^{\frac {1}{9} \left (-45-9 e^x+13 x\right )} x+4 e^{\frac {1}{9} \left (-45-9 e^x+13 x\right )} x^2\right ) \, dx\right )+\frac {4}{9} \int e^{\frac {1}{9} \left (-45-9 e^x+4 x\right )} x^2 \, dx-\frac {10}{9} \int e^{\frac {1}{9} \left (-45-9 e^x+4 x\right )} x \, dx-\frac {14}{9} \int e^{\frac {1}{9} \left (-45-9 e^x+4 x\right )} \, dx\\ &=\frac {4}{9} \int e^{\frac {1}{9} \left (-45-9 e^x+4 x\right )} x^2 \, dx-\frac {10}{9} \int e^{\frac {1}{9} \left (-45-9 e^x+4 x\right )} x \, dx-\frac {14}{9} \int e^{\frac {1}{9} \left (-45-9 e^x+4 x\right )} \, dx+7 \int e^{\frac {1}{9} \left (-45-9 e^x+13 x\right )} x \, dx-\frac {49}{4} \int e^{\frac {1}{9} \left (-45-9 e^x+13 x\right )} \, dx-\int e^{\frac {1}{9} \left (-45-9 e^x+13 x\right )} x^2 \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.32, size = 25, normalized size = 0.89 \begin {gather*} \frac {1}{4} e^{-5-e^x+\frac {4 x}{9}} (-7+2 x)^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 22, normalized size = 0.79 \begin {gather*} \frac {1}{4} \, {\left (4 \, x^{2} - 28 \, x + 49\right )} e^{\left (\frac {4}{9} \, x - e^{x} - 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.17, size = 42, normalized size = 1.50 \begin {gather*} \frac {1}{4} \, {\left (4 \, x^{2} e^{\left (\frac {4}{9} \, x - e^{x}\right )} - 28 \, x e^{\left (\frac {4}{9} \, x - e^{x}\right )} + 49 \, e^{\left (\frac {4}{9} \, x - e^{x}\right )}\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 20, normalized size = 0.71
method | result | size |
norman | \(\left (x^{2}-7 x +\frac {49}{4}\right ) {\mathrm e}^{-{\mathrm e}^{x}+\frac {4 x}{9}-5}\) | \(20\) |
risch | \(\frac {\left (36 x^{2}-252 x +441\right ) {\mathrm e}^{-{\mathrm e}^{x}+\frac {4 x}{9}-5}}{36}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {1}{36} \, \int {\left (16 \, x^{2} - 9 \, {\left (4 \, x^{2} - 28 \, x + 49\right )} e^{x} - 40 \, x - 56\right )} e^{\left (\frac {4}{9} \, x - e^{x} - 5\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.34, size = 20, normalized size = 0.71 \begin {gather*} \frac {{\mathrm {e}}^{\frac {4\,x}{9}}\,{\mathrm {e}}^{-5}\,{\mathrm {e}}^{-{\mathrm {e}}^x}\,{\left (2\,x-7\right )}^2}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.22, size = 22, normalized size = 0.79 \begin {gather*} \frac {\left (4 x^{2} - 28 x + 49\right ) e^{\frac {4 x}{9} - e^{x} - 5}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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