Optimal. Leaf size=21 \[ e^{(-1+x) \left (1-16 x^2-\frac {\log (9)}{4}\right )} x \]
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Rubi [B] time = 0.15, antiderivative size = 62, normalized size of antiderivative = 2.95, number of steps used = 3, number of rules used = 3, integrand size = 53, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.057, Rules used = {6, 12, 2288} \begin {gather*} \frac {3^{\frac {1-x}{2}} e^{-16 x^3+16 x^2+x-1} \left (-192 x^3+128 x^2+x (4-\log (9))\right )}{-192 x^2+128 x+4-\log (9)} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {1}{4} \exp \left (\frac {1}{4} \left (-4+4 x+64 x^2-64 x^3+(1-x) \log (9)\right )\right ) \left (4+128 x^2-192 x^3+x (4-\log (9))\right ) \, dx\\ &=\frac {1}{4} \int \exp \left (\frac {1}{4} \left (-4+4 x+64 x^2-64 x^3+(1-x) \log (9)\right )\right ) \left (4+128 x^2-192 x^3+x (4-\log (9))\right ) \, dx\\ &=\frac {3^{\frac {1-x}{2}} e^{-1+x+16 x^2-16 x^3} \left (128 x^2-192 x^3+x (4-\log (9))\right )}{4+128 x-192 x^2-\log (9)}\\ \end {aligned} \end {gather*}
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Mathematica [F] time = 1.29, size = 56, normalized size = 2.67 \begin {gather*} \frac {1}{4} \int e^{\frac {1}{4} \left (-4+4 x+64 x^2-64 x^3+(1-x) \log (9)\right )} \left (4+4 x+128 x^2-192 x^3-x \log (9)\right ) \, dx \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 23, normalized size = 1.10 \begin {gather*} x e^{\left (-16 \, x^{3} + 16 \, x^{2} - \frac {1}{2} \, {\left (x - 1\right )} \log \relax (3) + x - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.30, size = 24, normalized size = 1.14 \begin {gather*} \sqrt {3} x e^{\left (-16 \, x^{3} + 16 \, x^{2} - \frac {1}{2} \, x \log \relax (3) + x - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 26, normalized size = 1.24
method | result | size |
gosper | \({\mathrm e}^{-\frac {x \ln \relax (3)}{2}+\frac {\ln \relax (3)}{2}-16 x^{3}+16 x^{2}+x -1} x\) | \(26\) |
norman | \(x \,{\mathrm e}^{\frac {\left (1-x \right ) \ln \relax (3)}{2}-16 x^{3}+16 x^{2}+x -1}\) | \(26\) |
risch | \(x 3^{-\frac {x}{2}+\frac {1}{2}} {\mathrm e}^{-\left (x -1\right ) \left (4 x -1\right ) \left (4 x +1\right )}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.03, size = 24, normalized size = 1.14 \begin {gather*} \sqrt {3} x e^{\left (-16 \, x^{3} + 16 \, x^{2} - \frac {1}{2} \, x \log \relax (3) + x - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.11, size = 28, normalized size = 1.33 \begin {gather*} \frac {\sqrt {3}\,x\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{16\,x^2}\,{\mathrm {e}}^{-16\,x^3}\,{\mathrm {e}}^x}{3^{x/2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 26, normalized size = 1.24 \begin {gather*} x e^{- 16 x^{3} + 16 x^{2} + x + \left (\frac {1}{2} - \frac {x}{2}\right ) \log {\relax (3 )} - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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