Integrand size = 35, antiderivative size = 20 \[ \int \frac {12 x-3 x^2+e \left (-64+64 x-16 x^2\right )}{e \left (4-4 x+x^2\right )} \, dx=x \left (-16-\frac {8}{x}-\frac {3 x}{e (-2+x)}\right ) \]
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Time = 0.02 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.20, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.086, Rules used = {12, 27, 1864} \[ \int \frac {12 x-3 x^2+e \left (-64+64 x-16 x^2\right )}{e \left (4-4 x+x^2\right )} \, dx=\frac {12}{e (2-x)}-\frac {(3+16 e) x}{e} \]
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Rule 12
Rule 27
Rule 1864
Rubi steps \begin{align*} \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{align*}
Time = 0.02 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {12 x-3 x^2+e \left (-64+64 x-16 x^2\right )}{e \left (4-4 x+x^2\right )} \, dx=-\frac {12}{e (-2+x)}-16 x-\frac {3 x}{e} \]
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Time = 0.63 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10
method | result | size |
default | \({\mathrm e}^{-1} \left (-16 x \,{\mathrm e}-3 x -\frac {12}{-2+x}\right )\) | \(22\) |
risch | \(-16 \,{\mathrm e}^{-1} x \,{\mathrm e}-3 \,{\mathrm e}^{-1} x -\frac {12 \,{\mathrm e}^{-1}}{-2+x}\) | \(23\) |
norman | \(\frac {-{\mathrm e}^{-1} \left (16 \,{\mathrm e}+3\right ) x^{2}+64}{-2+x}\) | \(24\) |
gosper | \(-\frac {\left (16 x^{2} {\mathrm e}+3 x^{2}-64 \,{\mathrm e}\right ) {\mathrm e}^{-1}}{-2+x}\) | \(29\) |
parallelrisch | \(-\frac {\left (16 x^{2} {\mathrm e}+3 x^{2}-64 \,{\mathrm e}\right ) {\mathrm e}^{-1}}{-2+x}\) | \(29\) |
meijerg | \(-8 \left (-4 \,{\mathrm e}-\frac {3}{4}\right ) {\mathrm e}^{-1} \left (-\frac {x \left (-\frac {3 x}{2}+6\right )}{6 \left (1-\frac {x}{2}\right )}-2 \ln \left (1-\frac {x}{2}\right )\right )+4 \,{\mathrm e}^{-1} \left (16 \,{\mathrm e}+3\right ) \left (\frac {x}{2-x}+\ln \left (1-\frac {x}{2}\right )\right )-\frac {16 x}{1-\frac {x}{2}}\) | \(73\) |
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Time = 0.24 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.50 \[ \int \frac {12 x-3 x^2+e \left (-64+64 x-16 x^2\right )}{e \left (4-4 x+x^2\right )} \, dx=-\frac {{\left (3 \, x^{2} + 16 \, {\left (x^{2} - 2 \, x\right )} e - 6 \, x + 12\right )} e^{\left (-1\right )}}{x - 2} \]
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Time = 0.07 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {12 x-3 x^2+e \left (-64+64 x-16 x^2\right )}{e \left (4-4 x+x^2\right )} \, dx=- x \left (\frac {3}{e} + 16\right ) - \frac {12}{e x - 2 e} \]
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Time = 0.19 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {12 x-3 x^2+e \left (-64+64 x-16 x^2\right )}{e \left (4-4 x+x^2\right )} \, dx=-{\left (x {\left (16 \, e + 3\right )} + \frac {12}{x - 2}\right )} e^{\left (-1\right )} \]
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Time = 0.25 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {12 x-3 x^2+e \left (-64+64 x-16 x^2\right )}{e \left (4-4 x+x^2\right )} \, dx=-{\left (16 \, x e + 3 \, x + \frac {12}{x - 2}\right )} e^{\left (-1\right )} \]
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Time = 0.09 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.30 \[ \int \frac {12 x-3 x^2+e \left (-64+64 x-16 x^2\right )}{e \left (4-4 x+x^2\right )} \, dx=\frac {12}{2\,\mathrm {e}-x\,\mathrm {e}}-x\,{\mathrm {e}}^{-1}\,\left (16\,\mathrm {e}+3\right ) \]
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