Optimal. Leaf size=18 \[ \frac {(-11+x) x \left (8+e^4+x\right )}{2-x} \]
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Rubi [A] time = 0.04, antiderivative size = 29, normalized size of antiderivative = 1.61, number of steps used = 3, number of rules used = 2, integrand size = 40, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {27, 1850} \begin {gather*} -x^2+\left (1-e^4\right ) x-\frac {18 \left (10+e^4\right )}{2-x} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 1850
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-176-12 x+9 x^2-2 x^3+e^4 \left (-22+4 x-x^2\right )}{(-2+x)^2} \, dx\\ &=\int \left (1-e^4-\frac {18 \left (10+e^4\right )}{(-2+x)^2}-2 x\right ) \, dx\\ &=-\frac {18 \left (10+e^4\right )}{2-x}+\left (1-e^4\right ) x-x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 30, normalized size = 1.67 \begin {gather*} \frac {18 \left (10+e^4\right )}{-2+x}-\left (3+e^4\right ) (-2+x)-(-2+x)^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 31, normalized size = 1.72 \begin {gather*} -\frac {x^{3} - 3 \, x^{2} + {\left (x^{2} - 2 \, x - 18\right )} e^{4} + 2 \, x - 180}{x - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.35, size = 23, normalized size = 1.28 \begin {gather*} -x^{2} - x e^{4} + x + \frac {18 \, {\left (e^{4} + 10\right )}}{x - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.22, size = 26, normalized size = 1.44
method | result | size |
default | \(-x^{2}+x -x \,{\mathrm e}^{4}-\frac {-180-18 \,{\mathrm e}^{4}}{x -2}\) | \(26\) |
gosper | \(-\frac {x^{2} {\mathrm e}^{4}+x^{3}-3 x^{2}-22 \,{\mathrm e}^{4}-176}{x -2}\) | \(28\) |
norman | \(\frac {\left (3-{\mathrm e}^{4}\right ) x^{2}-x^{3}+176+22 \,{\mathrm e}^{4}}{x -2}\) | \(28\) |
risch | \(-x \,{\mathrm e}^{4}-x^{2}+x +\frac {18 \,{\mathrm e}^{4}}{x -2}+\frac {180}{x -2}\) | \(29\) |
meijerg | \(-\frac {44 x}{1-\frac {x}{2}}-2 \left (-{\mathrm e}^{4}+9\right ) \left (-\frac {x \left (-\frac {3 x}{2}+6\right )}{6 \left (1-\frac {x}{2}\right )}-2 \ln \left (1-\frac {x}{2}\right )\right )-2 \left (-2 \,{\mathrm e}^{4}+6\right ) \left (\frac {x}{2-x}+\ln \left (1-\frac {x}{2}\right )\right )-\frac {x \left (-\frac {1}{2} x^{2}-3 x +12\right )}{1-\frac {x}{2}}-24 \ln \left (1-\frac {x}{2}\right )-\frac {11 \,{\mathrm e}^{4} x}{2 \left (1-\frac {x}{2}\right )}\) | \(109\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 24, normalized size = 1.33 \begin {gather*} -x^{2} - x {\left (e^{4} - 1\right )} + \frac {18 \, {\left (e^{4} + 10\right )}}{x - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.78, size = 25, normalized size = 1.39 \begin {gather*} \frac {18\,{\mathrm {e}}^4+180}{x-2}-x\,\left ({\mathrm {e}}^4-1\right )-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 22, normalized size = 1.22 \begin {gather*} - x^{2} - x \left (-1 + e^{4}\right ) - \frac {- 18 e^{4} - 180}{x - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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