Optimal. Leaf size=29 \[ x \left (x-(2-x)^2 \left (-2-e^{3/4}+\frac {1}{x}-\log (2)\right )\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 50, normalized size of antiderivative = 1.72, number of steps used = 3, number of rules used = 1, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {6} \begin {gather*} 2 x^3+x^3 \left (e^{3/4}+\log (2)\right )-8 x^2-4 x^2 \left (e^{3/4}+\log (2)\right )+12 x+4 x \left (e^{3/4}+\log (2)\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (12-16 x+6 x^2+\left (4-8 x+3 x^2\right ) \left (e^{3/4}+\log (2)\right )\right ) \, dx\\ &=12 x-8 x^2+2 x^3+\left (e^{3/4}+\log (2)\right ) \int \left (4-8 x+3 x^2\right ) \, dx\\ &=12 x-8 x^2+2 x^3+4 x \left (e^{3/4}+\log (2)\right )-4 x^2 \left (e^{3/4}+\log (2)\right )+x^3 \left (e^{3/4}+\log (2)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 36, normalized size = 1.24 \begin {gather*} \frac {1}{3} x \left (36+3 e^{3/4} (-2+x)^2-12 x (2+\log (2))+x^2 (6+\log (8))+\log (4096)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.49, size = 44, normalized size = 1.52 \begin {gather*} 2 \, x^{3} - 8 \, x^{2} + {\left (x^{3} - 4 \, x^{2} + 4 \, x\right )} e^{\frac {3}{4}} + {\left (x^{3} - 4 \, x^{2} + 4 \, x\right )} \log \relax (2) + 12 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 44, normalized size = 1.52 \begin {gather*} 2 \, x^{3} - 8 \, x^{2} + {\left (x^{3} - 4 \, x^{2} + 4 \, x\right )} e^{\frac {3}{4}} + {\left (x^{3} - 4 \, x^{2} + 4 \, x\right )} \log \relax (2) + 12 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 38, normalized size = 1.31
method | result | size |
norman | \(\left ({\mathrm e}^{\frac {3}{4}}+\ln \relax (2)+2\right ) x^{3}+\left (-4 \ln \relax (2)-4 \,{\mathrm e}^{\frac {3}{4}}-8\right ) x^{2}+\left (4 \ln \relax (2)+4 \,{\mathrm e}^{\frac {3}{4}}+12\right ) x\) | \(38\) |
gosper | \(x \left (x^{2} \ln \relax (2)+x^{2} {\mathrm e}^{\frac {3}{4}}-4 x \ln \relax (2)-4 x \,{\mathrm e}^{\frac {3}{4}}+2 x^{2}+4 \ln \relax (2)+4 \,{\mathrm e}^{\frac {3}{4}}-8 x +12\right )\) | \(43\) |
default | \(\ln \relax (2) \left (x^{3}-4 x^{2}+4 x \right )+{\mathrm e}^{\frac {3}{4}} \left (x^{3}-4 x^{2}+4 x \right )+2 x^{3}-8 x^{2}+12 x\) | \(45\) |
risch | \(x^{3} \ln \relax (2)-4 x^{2} \ln \relax (2)+4 x \ln \relax (2)+{\mathrm e}^{\frac {3}{4}} x^{3}-4 x^{2} {\mathrm e}^{\frac {3}{4}}+4 x \,{\mathrm e}^{\frac {3}{4}}+2 x^{3}-8 x^{2}+12 x\) | \(51\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 44, normalized size = 1.52 \begin {gather*} 2 \, x^{3} - 8 \, x^{2} + {\left (x^{3} - 4 \, x^{2} + 4 \, x\right )} e^{\frac {3}{4}} + {\left (x^{3} - 4 \, x^{2} + 4 \, x\right )} \log \relax (2) + 12 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 34, normalized size = 1.17 \begin {gather*} \left ({\mathrm {e}}^{3/4}+\ln \relax (2)+2\right )\,x^3+\left (-4\,{\mathrm {e}}^{3/4}-\ln \left (16\right )-8\right )\,x^2+\left (4\,{\mathrm {e}}^{3/4}+\ln \left (16\right )+12\right )\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.06, size = 46, normalized size = 1.59 \begin {gather*} x^{3} \left (\log {\relax (2 )} + 2 + e^{\frac {3}{4}}\right ) + x^{2} \left (- 4 e^{\frac {3}{4}} - 8 - 4 \log {\relax (2 )}\right ) + x \left (4 \log {\relax (2 )} + 4 e^{\frac {3}{4}} + 12\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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