Optimal. Leaf size=20 \[ x \left (-16-\frac {8}{x}-\frac {3 x}{e (-2+x)}\right ) \]
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Rubi [A] time = 0.03, antiderivative size = 24, normalized size of antiderivative = 1.20, number of steps used = 4, number of rules used = 3, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.086, Rules used = {12, 27, 1850} \begin {gather*} \frac {12}{e (2-x)}-\frac {(3+16 e) x}{e} \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 {12 x-3 x^2+e \left (-64+64 x-16 x^2\right )}{4-4 x+x^2} \, dx}{e}\\ &=\frac {\int \frac {12 x-3 x^2+e \left (-64+64 x-16 x^2\right )}{(-2+x)^2} \, dx}{e}\\ &=\frac {\int \left (-3-16 e+\frac {12}{(-2+x)^2}\right ) \, dx}{e}\\ &=\frac {12}{e (2-x)}-\frac {(3+16 e) x}{e}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 20, normalized size = 1.00 \begin {gather*} -\frac {12}{e (-2+x)}-16 x-\frac {3 x}{e} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.47, size = 30, normalized size = 1.50 \begin {gather*} -\frac {{\left (3 \, x^{2} + 16 \, {\left (x^{2} - 2 \, x\right )} e - 6 \, x + 12\right )} e^{\left (-1\right )}}{x - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 20, normalized size = 1.00 \begin {gather*} -{\left (16 \, x e + 3 \, x + \frac {12}{x - 2}\right )} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.49, size = 22, normalized size = 1.10
method | result | size |
default | \({\mathrm e}^{-1} \left (-16 x \,{\mathrm e}-3 x -\frac {12}{x -2}\right )\) | \(22\) |
risch | \(-16 \,{\mathrm e}^{-1} x \,{\mathrm e}-3 \,{\mathrm e}^{-1} x -\frac {12 \,{\mathrm e}^{-1}}{x -2}\) | \(23\) |
norman | \(\frac {-{\mathrm e}^{-1} \left (16 \,{\mathrm e}+3\right ) x^{2}+64}{x -2}\) | \(24\) |
gosper | \(-\frac {\left (16 x^{2} {\mathrm e}+3 x^{2}-64 \,{\mathrm e}\right ) {\mathrm e}^{-1}}{x -2}\) | \(29\) |
meijerg | \(-2 \left (-16 \,{\mathrm e}-3\right ) {\mathrm e}^{-1} \left (-\frac {x \left (-\frac {3 x}{2}+6\right )}{6 \left (1-\frac {x}{2}\right )}-2 \ln \left (1-\frac {x}{2}\right )\right )+\left (64 \,{\mathrm e}+12\right ) {\mathrm e}^{-1} \left (\frac {x}{2-x}+\ln \left (1-\frac {x}{2}\right )\right )-\frac {16 x}{1-\frac {x}{2}}\) | \(72\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 20, normalized size = 1.00 \begin {gather*} -{\left (x {\left (16 \, e + 3\right )} + \frac {12}{x - 2}\right )} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.11, size = 26, normalized size = 1.30 \begin {gather*} \frac {12}{2\,\mathrm {e}-x\,\mathrm {e}}-x\,{\mathrm {e}}^{-1}\,\left (16\,\mathrm {e}+3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 20, normalized size = 1.00 \begin {gather*} - x \left (\frac {3}{e} + 16\right ) - \frac {12}{e x - 2 e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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