Optimal. Leaf size=29 \[ \frac {1}{5} e^{\frac {3 e^{e^{-9-x} x} x^2}{1-x}} \]
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Rubi [F] time = 8.29, 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 {\exp \left (-9-x+e^{-9-x} x-\frac {3 e^{e^{-9-x} x} x^2}{-1+x}\right ) \left (3 x^2-6 x^3+3 x^4+e^{9+x} \left (6 x-3 x^2\right )\right )}{5-10 x+5 x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (-9-x+e^{-9-x} x-\frac {3 e^{e^{-9-x} x} x^2}{-1+x}\right ) \left (3 x^2-6 x^3+3 x^4+e^{9+x} \left (6 x-3 x^2\right )\right )}{5 (-1+x)^2} \, dx\\ &=\frac {1}{5} \int \frac {\exp \left (-9-x+e^{-9-x} x-\frac {3 e^{e^{-9-x} x} x^2}{-1+x}\right ) \left (3 x^2-6 x^3+3 x^4+e^{9+x} \left (6 x-3 x^2\right )\right )}{(-1+x)^2} \, dx\\ &=\frac {1}{5} \int \frac {3 \exp \left (-9-x+e^{-9-x} x-\frac {3 e^{e^{-9-x} x} x^2}{-1+x}\right ) x \left (2 e^{9+x}+x-e^{9+x} x-2 x^2+x^3\right )}{(1-x)^2} \, dx\\ &=\frac {3}{5} \int \frac {\exp \left (-9-x+e^{-9-x} x-\frac {3 e^{e^{-9-x} x} x^2}{-1+x}\right ) x \left (2 e^{9+x}+x-e^{9+x} x-2 x^2+x^3\right )}{(1-x)^2} \, dx\\ &=\frac {3}{5} \int \left (-\frac {e^{e^{-9-x} x-\frac {3 e^{e^{-9-x} x} x^2}{-1+x}} (-2+x) x}{(-1+x)^2}+\exp \left (-9-x+e^{-9-x} x-\frac {3 e^{e^{-9-x} x} x^2}{-1+x}\right ) x^2\right ) \, dx\\ &=-\left (\frac {3}{5} \int \frac {e^{e^{-9-x} x-\frac {3 e^{e^{-9-x} x} x^2}{-1+x}} (-2+x) x}{(-1+x)^2} \, dx\right )+\frac {3}{5} \int \exp \left (-9-x+e^{-9-x} x-\frac {3 e^{e^{-9-x} x} x^2}{-1+x}\right ) x^2 \, dx\\ &=-\left (\frac {3}{5} \int \left (e^{e^{-9-x} x-\frac {3 e^{e^{-9-x} x} x^2}{-1+x}}-\frac {e^{e^{-9-x} x-\frac {3 e^{e^{-9-x} x} x^2}{-1+x}}}{(-1+x)^2}\right ) \, dx\right )+\frac {3}{5} \int \exp \left (-9-x+e^{-9-x} x-\frac {3 e^{e^{-9-x} x} x^2}{-1+x}\right ) x^2 \, dx\\ &=-\left (\frac {3}{5} \int e^{e^{-9-x} x-\frac {3 e^{e^{-9-x} x} x^2}{-1+x}} \, dx\right )+\frac {3}{5} \int \frac {e^{e^{-9-x} x-\frac {3 e^{e^{-9-x} x} x^2}{-1+x}}}{(-1+x)^2} \, dx+\frac {3}{5} \int \exp \left (-9-x+e^{-9-x} x-\frac {3 e^{e^{-9-x} x} x^2}{-1+x}\right ) x^2 \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.84, size = 27, normalized size = 0.93 \begin {gather*} \frac {1}{5} e^{-\frac {3 e^{e^{-9-x} x} x^2}{-1+x}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 1.07, size = 65, normalized size = 2.24 \begin {gather*} \frac {1}{5} \, e^{\left (-x e^{\left (-x - 9\right )} + x - \frac {{\left (3 \, x^{2} e^{\left (x e^{\left (-x - 9\right )} + x + 9\right )} - x^{2} + {\left (x^{2} + 8 \, x - 9\right )} e^{\left (x + 9\right )} + x\right )} e^{\left (-x - 9\right )}}{x - 1} + 9\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {3 \, {\left (x^{4} - 2 \, x^{3} + x^{2} - {\left (x^{2} - 2 \, x\right )} e^{\left (x + 9\right )}\right )} e^{\left (-\frac {3 \, x^{2} e^{\left (x e^{\left (-x - 9\right )}\right )}}{x - 1} + x e^{\left (-x - 9\right )} - x - 9\right )}}{5 \, {\left (x^{2} - 2 \, x + 1\right )}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.14, size = 23, normalized size = 0.79
method | result | size |
risch | \(\frac {{\mathrm e}^{-\frac {3 x^{2} {\mathrm e}^{x \,{\mathrm e}^{-x -9}}}{x -1}}}{5}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 43, normalized size = 1.48 \begin {gather*} \frac {1}{5} \, e^{\left (-3 \, x e^{\left (x e^{\left (-x - 9\right )}\right )} - \frac {3 \, e^{\left (x e^{\left (-x - 9\right )}\right )}}{x - 1} - 3 \, e^{\left (x e^{\left (-x - 9\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.38, size = 22, normalized size = 0.76 \begin {gather*} \frac {{\mathrm {e}}^{-\frac {3\,x^2\,{\mathrm {e}}^{x\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-9}}}{x-1}}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.66, size = 22, normalized size = 0.76 \begin {gather*} \frac {e^{- \frac {3 x^{2} e^{x e^{- x - 9}}}{x - 1}}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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