Optimal. Leaf size=25 \[ -1-e^{(x+\log (3)) (x+(-2+x) x-\log (4))}+2 x \]
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Rubi [A]
time = 0.34, antiderivative size = 36, normalized size of antiderivative = 1.44, number of steps
used = 2, number of rules used = 1, integrand size = 54, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {6838}
\begin {gather*} 2 x-3^{x^2-x} e^{x^3-x^2} 4^{-x-\log (3)} \end {gather*}
Antiderivative was successfully verified.
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Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 x+\int \exp \left (-x^2+x^3+\left (-x+x^2\right ) \log (3)+(-x-\log (3)) \log (4)\right ) \left (2 x-3 x^2+(1-2 x) \log (3)+\log (4)\right ) \, dx\\ &=-3^{-x+x^2} 4^{-x-\log (3)} e^{-x^2+x^3}+2 x\\ \end {aligned} \end {gather*}
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Mathematica [F]
time = 0.55, size = 0, normalized size = 0.00 \begin {gather*} \int \left (2+e^{-x^2+x^3+\left (-x+x^2\right ) \log (3)+(-x-\log (3)) \log (4)} \left (2 x-3 x^2+(1-2 x) \log (3)+\log (4)\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.73, size = 39, normalized size = 1.56
method | result | size |
risch | \(2 x -2^{-2 \ln \left (3\right )-2 x} 3^{x \left (x -1\right )} {\mathrm e}^{x^{2} \left (x -1\right )}\) | \(32\) |
default | \(2 x -{\mathrm e}^{2 \left (-\ln \left (3\right )-x \right ) \ln \left (2\right )+\left (x^{2}-x \right ) \ln \left (3\right )+x^{3}-x^{2}}\) | \(39\) |
norman | \(2 x -{\mathrm e}^{2 \left (-\ln \left (3\right )-x \right ) \ln \left (2\right )+\left (x^{2}-x \right ) \ln \left (3\right )+x^{3}-x^{2}}\) | \(39\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 34, normalized size = 1.36 \begin {gather*} 2 \, x - e^{\left (x^{3} - x^{2} + {\left (x^{2} - x\right )} \log \left (3\right ) - 2 \, {\left (x + \log \left (3\right )\right )} \log \left (2\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 35, normalized size = 1.40 \begin {gather*} 2 \, x - e^{\left (x^{3} - x^{2} + {\left (x^{2} - x - 2 \, \log \left (2\right )\right )} \log \left (3\right ) - 2 \, x \log \left (2\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 32, normalized size = 1.28 \begin {gather*} 2 x - e^{x^{3} - x^{2} + \left (- 2 x - 2 \log {\left (3 \right )}\right ) \log {\left (2 \right )} + \left (x^{2} - x\right ) \log {\left (3 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 38, normalized size = 1.52 \begin {gather*} 2 \, x - e^{\left (x^{3} + x^{2} \log \left (3\right ) - x^{2} - x \log \left (3\right ) - 2 \, x \log \left (2\right ) - 2 \, \log \left (3\right ) \log \left (2\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.16, size = 41, normalized size = 1.64 \begin {gather*} 2\,x-\frac {3^{x^2}\,{\mathrm {e}}^{x^3-x^2}}{2^{2\,\ln \left (3\right )}\,2^{2\,x}\,3^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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