Optimal. Leaf size=22 \[ \frac {1}{2} e^{4-2 x+e^{6 x} x} (-1+x) x \]
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Rubi [F] time = 1.12, 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}{2} \exp \left (6 x+e^{6 x} \left (e^{-6 x} (4-2 x)+x\right )\right ) \left (-x-5 x^2+6 x^3+e^{-6 x} \left (-1+4 x-2 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}{2} \int \exp \left (6 x+e^{6 x} \left (e^{-6 x} (4-2 x)+x\right )\right ) \left (-x-5 x^2+6 x^3+e^{-6 x} \left (-1+4 x-2 x^2\right )\right ) \, dx\\ &=\frac {1}{2} \int \left (-\exp \left (6 x+e^{6 x} \left (e^{-6 x} (4-2 x)+x\right )\right ) x-5 \exp \left (6 x+e^{6 x} \left (e^{-6 x} (4-2 x)+x\right )\right ) x^2+6 \exp \left (6 x+e^{6 x} \left (e^{-6 x} (4-2 x)+x\right )\right ) x^3-e^{e^{6 x} \left (e^{-6 x} (4-2 x)+x\right )} \left (1-4 x+2 x^2\right )\right ) \, dx\\ &=-\left (\frac {1}{2} \int \exp \left (6 x+e^{6 x} \left (e^{-6 x} (4-2 x)+x\right )\right ) x \, dx\right )-\frac {1}{2} \int e^{e^{6 x} \left (e^{-6 x} (4-2 x)+x\right )} \left (1-4 x+2 x^2\right ) \, dx-\frac {5}{2} \int \exp \left (6 x+e^{6 x} \left (e^{-6 x} (4-2 x)+x\right )\right ) x^2 \, dx+3 \int \exp \left (6 x+e^{6 x} \left (e^{-6 x} (4-2 x)+x\right )\right ) x^3 \, dx\\ &=-\left (\frac {1}{2} \int e^{4+\left (4+e^{6 x}\right ) x} x \, dx\right )-\frac {1}{2} \int e^{4+\left (-2+e^{6 x}\right ) x} \left (1-4 x+2 x^2\right ) \, dx-\frac {5}{2} \int e^{4+\left (4+e^{6 x}\right ) x} x^2 \, dx+3 \int e^{4+\left (4+e^{6 x}\right ) x} x^3 \, dx\\ &=-\left (\frac {1}{2} \int e^{4+\left (4+e^{6 x}\right ) x} x \, dx\right )-\frac {1}{2} \int \left (e^{4+\left (-2+e^{6 x}\right ) x}-4 e^{4+\left (-2+e^{6 x}\right ) x} x+2 e^{4+\left (-2+e^{6 x}\right ) x} x^2\right ) \, dx-\frac {5}{2} \int e^{4+\left (4+e^{6 x}\right ) x} x^2 \, dx+3 \int e^{4+\left (4+e^{6 x}\right ) x} x^3 \, dx\\ &=-\left (\frac {1}{2} \int e^{4+\left (-2+e^{6 x}\right ) x} \, dx\right )-\frac {1}{2} \int e^{4+\left (4+e^{6 x}\right ) x} x \, dx+2 \int e^{4+\left (-2+e^{6 x}\right ) x} x \, dx-\frac {5}{2} \int e^{4+\left (4+e^{6 x}\right ) x} x^2 \, dx+3 \int e^{4+\left (4+e^{6 x}\right ) x} x^3 \, dx-\int e^{4+\left (-2+e^{6 x}\right ) x} x^2 \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.42, size = 21, normalized size = 0.95 \begin {gather*} \frac {1}{2} e^{4+\left (-2+e^{6 x}\right ) x} (-1+x) x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 21, normalized size = 0.95 \begin {gather*} \frac {1}{2} \, {\left (x^{2} - x\right )} e^{\left (x e^{\left (6 \, x\right )} - 2 \, x + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.35, size = 38, normalized size = 1.73 \begin {gather*} \frac {1}{2} \, {\left (x^{2} e^{\left (x e^{\left (6 \, x\right )} + 4 \, x + 4\right )} - x e^{\left (x e^{\left (6 \, x\right )} + 4 \, x + 4\right )}\right )} e^{\left (-6 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 31, normalized size = 1.41
method | result | size |
risch | \(\frac {x \left (x -1\right ) {\mathrm e}^{-\left (2 \,{\mathrm e}^{-6 x} x -4 \,{\mathrm e}^{-6 x}-x \right ) {\mathrm e}^{6 x}}}{2}\) | \(31\) |
norman | \(\left (-\frac {{\mathrm e}^{-6 x} x \,{\mathrm e}^{\left (\left (4-2 x \right ) {\mathrm e}^{-6 x}+x \right ) {\mathrm e}^{6 x}}}{2}+\frac {{\mathrm e}^{-6 x} x^{2} {\mathrm e}^{\left (\left (4-2 x \right ) {\mathrm e}^{-6 x}+x \right ) {\mathrm e}^{6 x}}}{2}\right ) {\mathrm e}^{6 x}\) | \(65\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.75, size = 25, normalized size = 1.14 \begin {gather*} \frac {1}{2} \, {\left (x^{2} e^{4} - x e^{4}\right )} e^{\left (x e^{\left (6 \, x\right )} - 2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.40, size = 19, normalized size = 0.86 \begin {gather*} \frac {x\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^4\,{\mathrm {e}}^{x\,{\mathrm {e}}^{6\,x}}\,\left (x-1\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.23, size = 24, normalized size = 1.09 \begin {gather*} \frac {\left (x^{2} - x\right ) e^{\left (x + \left (4 - 2 x\right ) e^{- 6 x}\right ) e^{6 x}}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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