Optimal. Leaf size=26 \[ -\frac {9 x^2}{16}+x \left (\frac {4}{e^4}+x-\frac {1}{-1+2 x}\right ) \]
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Rubi [A] time = 0.04, antiderivative size = 25, normalized size of antiderivative = 0.96, number of steps used = 5, number of rules used = 3, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {12, 27, 1850} \begin {gather*} \frac {7 x^2}{16}+\frac {4 x}{e^4}+\frac {1}{2 (1-2 x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 1850
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {32-128 x+128 x^2+e^4 \left (8+7 x-28 x^2+28 x^3\right )}{8-32 x+32 x^2} \, dx}{e^4}\\ &=\frac {\int \frac {32-128 x+128 x^2+e^4 \left (8+7 x-28 x^2+28 x^3\right )}{8 (-1+2 x)^2} \, dx}{e^4}\\ &=\frac {\int \frac {32-128 x+128 x^2+e^4 \left (8+7 x-28 x^2+28 x^3\right )}{(-1+2 x)^2} \, dx}{8 e^4}\\ &=\frac {\int \left (32+7 e^4 x+\frac {8 e^4}{(-1+2 x)^2}\right ) \, dx}{8 e^4}\\ &=\frac {1}{2 (1-2 x)}+\frac {4 x}{e^4}+\frac {7 x^2}{16}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 24, normalized size = 0.92 \begin {gather*} -\frac {7}{64}+\frac {1}{2-4 x}+\frac {4 x}{e^4}+\frac {7 x^2}{16} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 35, normalized size = 1.35 \begin {gather*} \frac {{\left (128 \, x^{2} + {\left (14 \, x^{3} - 7 \, x^{2} - 8\right )} e^{4} - 64 \, x\right )} e^{\left (-4\right )}}{16 \, {\left (2 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 26, normalized size = 1.00 \begin {gather*} \frac {1}{16} \, {\left (7 \, x^{2} e^{4} + 64 \, x - \frac {8 \, e^{4}}{2 \, x - 1}\right )} e^{\left (-4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.40, size = 19, normalized size = 0.73
method | result | size |
risch | \(\frac {7 x^{2}}{16}+4 x \,{\mathrm e}^{-4}-\frac {1}{4 \left (x -\frac {1}{2}\right )}\) | \(19\) |
default | \(\frac {{\mathrm e}^{-4} \left (32 x +\frac {7 x^{2} {\mathrm e}^{4}}{2}-\frac {4 \,{\mathrm e}^{4}}{2 x -1}\right )}{8}\) | \(29\) |
gosper | \(\frac {\left (14 x^{3} {\mathrm e}^{4}-7 x^{2} {\mathrm e}^{4}+128 x^{2}-8 \,{\mathrm e}^{4}-32\right ) {\mathrm e}^{-4}}{32 x -16}\) | \(39\) |
norman | \(\frac {-\left (4+{\mathrm e}^{4}\right ) {\mathrm e}^{-4} x +\frac {7 x^{3}}{8}-\frac {\left (7 \,{\mathrm e}^{4}-128\right ) {\mathrm e}^{-4} x^{2}}{16}}{2 x -1}\) | \(41\) |
meijerg | \(\frac {4 \,{\mathrm e}^{-4} x}{1-2 x}+\frac {7 x \left (-8 x^{2}-12 x +12\right )}{64 \left (1-2 x \right )}+\frac {21 \ln \left (1-2 x \right )}{32}-\frac {\left (-28 \,{\mathrm e}^{4}+128\right ) {\mathrm e}^{-4} \left (-\frac {2 x \left (6-6 x \right )}{3 \left (1-2 x \right )}-2 \ln \left (1-2 x \right )\right )}{64}+\frac {\left (7 \,{\mathrm e}^{4}-128\right ) {\mathrm e}^{-4} \left (\frac {2 x}{1-2 x}+\ln \left (1-2 x \right )\right )}{32}+\frac {x}{1-2 x}\) | \(112\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 26, normalized size = 1.00 \begin {gather*} \frac {1}{16} \, {\left (7 \, x^{2} e^{4} + 64 \, x - \frac {8 \, e^{4}}{2 \, x - 1}\right )} e^{\left (-4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 20, normalized size = 0.77 \begin {gather*} 4\,x\,{\mathrm {e}}^{-4}-\frac {1}{4\,\left (x-\frac {1}{2}\right )}+\frac {7\,x^2}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 19, normalized size = 0.73 \begin {gather*} \frac {7 x^{2}}{16} + \frac {4 x}{e^{4}} - \frac {1}{4 x - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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