Optimal. Leaf size=30 \[ -4 x+e^{\frac {7}{6} (-2+x) x^2} (i \pi +\log (2-\log (2))) \]
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Rubi [A] time = 0.14, antiderivative size = 35, normalized size of antiderivative = 1.17, number of steps used = 4, number of rules used = 3, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.065, Rules used = {12, 1593, 6706} \begin {gather*} -4 x+e^{-\frac {7}{6} \left (2 x^2-x^3\right )} (\log (2-\log (2))+i \pi ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 1593
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{6} \int \left (-24+e^{\frac {1}{6} \left (-14 x^2+7 x^3\right )} \left (-28 x+21 x^2\right ) (i \pi +\log (2-\log (2)))\right ) \, dx\\ &=-4 x+\frac {1}{6} (i \pi +\log (2-\log (2))) \int e^{\frac {1}{6} \left (-14 x^2+7 x^3\right )} \left (-28 x+21 x^2\right ) \, dx\\ &=-4 x+\frac {1}{6} (i \pi +\log (2-\log (2))) \int e^{\frac {1}{6} \left (-14 x^2+7 x^3\right )} x (-28+21 x) \, dx\\ &=-4 x+e^{-\frac {7}{6} \left (2 x^2-x^3\right )} (i \pi +\log (2-\log (2)))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.07, size = 35, normalized size = 1.17 \begin {gather*} -4 x+e^{-\frac {7 x^2}{3}+\frac {7 x^3}{6}} (i \pi +\log (2-\log (2))) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 22, normalized size = 0.73 \begin {gather*} e^{\left (\frac {7}{6} \, x^{3} - \frac {7}{3} \, x^{2}\right )} \log \left (\log \relax (2) - 2\right ) - 4 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.29, size = 22, normalized size = 0.73 \begin {gather*} e^{\left (\frac {7}{6} \, x^{3} - \frac {7}{3} \, x^{2}\right )} \log \left (\log \relax (2) - 2\right ) - 4 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 20, normalized size = 0.67
method | result | size |
risch | \(\ln \left (\ln \relax (2)-2\right ) {\mathrm e}^{\frac {7 \left (x -2\right ) x^{2}}{6}}-4 x\) | \(20\) |
default | \(-4 x +{\mathrm e}^{\frac {7}{6} x^{3}-\frac {7}{3} x^{2}} \ln \left (\ln \relax (2)-2\right )\) | \(23\) |
norman | \(-4 x +{\mathrm e}^{\frac {7}{6} x^{3}-\frac {7}{3} x^{2}} \ln \left (\ln \relax (2)-2\right )\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 22, normalized size = 0.73 \begin {gather*} e^{\left (\frac {7}{6} \, x^{3} - \frac {7}{3} \, x^{2}\right )} \log \left (\log \relax (2) - 2\right ) - 4 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.10, size = 22, normalized size = 0.73 \begin {gather*} \ln \left (\ln \relax (2)-2\right )\,{\mathrm {e}}^{\frac {7\,x^3}{6}-\frac {7\,x^2}{3}}-4\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 3.54, size = 41, normalized size = 1.37 \begin {gather*} - 4 x - \left (- e^{- \frac {7 x^{2}}{3}} \log {\left (2 - \log {\relax (2 )} \right )} - i \pi e^{- \frac {7 x^{2}}{3}}\right ) e^{\frac {7 x^{3}}{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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