Optimal. Leaf size=16 \[ \frac {-4+x}{19+e^2-\frac {11 x}{2}} \]
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Rubi [A] time = 0.02, antiderivative size = 24, normalized size of antiderivative = 1.50, number of steps used = 4, number of rules used = 4, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {12, 1981, 27, 32} \begin {gather*} -\frac {4 \left (3-e^2\right )}{11 \left (2 \left (19+e^2\right )-11 x\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 32
Rule 1981
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (\left (4 \left (3-e^2\right )\right ) \int \frac {1}{1444+4 e^4+e^2 (152-44 x)-836 x+121 x^2} \, dx\right )\\ &=-\left (\left (4 \left (3-e^2\right )\right ) \int \frac {1}{4 \left (19+e^2\right )^2-44 \left (19+e^2\right ) x+121 x^2} \, dx\right )\\ &=-\left (\left (4 \left (3-e^2\right )\right ) \int \frac {1}{\left (38+2 e^2-11 x\right )^2} \, dx\right )\\ &=-\frac {4 \left (3-e^2\right )}{11 \left (2 \left (19+e^2\right )-11 x\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 19, normalized size = 1.19 \begin {gather*} \frac {4 \left (-3+e^2\right )}{418+22 e^2-121 x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 17, normalized size = 1.06 \begin {gather*} -\frac {4 \, {\left (e^{2} - 3\right )}}{11 \, {\left (11 \, x - 2 \, e^{2} - 38\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: NotImplementedError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 9.31, size = 18, normalized size = 1.12
method | result | size |
gosper | \(\frac {-\frac {12}{11}+\frac {4 \,{\mathrm e}^{2}}{11}}{2 \,{\mathrm e}^{2}-11 x +38}\) | \(18\) |
norman | \(\frac {-\frac {12}{11}+\frac {4 \,{\mathrm e}^{2}}{11}}{2 \,{\mathrm e}^{2}-11 x +38}\) | \(19\) |
risch | \(\frac {2 \,{\mathrm e}^{2}}{11 \left (19-\frac {11 x}{2}+{\mathrm e}^{2}\right )}-\frac {6}{11 \left (19-\frac {11 x}{2}+{\mathrm e}^{2}\right )}\) | \(26\) |
meijerg | \(\frac {6 x}{11 \left (-\frac {2 \,{\mathrm e}^{2}}{11}-\frac {38}{11}\right ) \left (1-\frac {11 x}{2 \left ({\mathrm e}^{2}+19\right )}\right ) \left ({\mathrm e}^{2}+19\right )}-\frac {2 \,{\mathrm e}^{2} x}{11 \left (-\frac {2 \,{\mathrm e}^{2}}{11}-\frac {38}{11}\right ) \left (1-\frac {11 x}{2 \left ({\mathrm e}^{2}+19\right )}\right ) \left ({\mathrm e}^{2}+19\right )}\) | \(64\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 17, normalized size = 1.06 \begin {gather*} -\frac {4 \, {\left (e^{2} - 3\right )}}{11 \, {\left (11 \, x - 2 \, e^{2} - 38\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.11, size = 18, normalized size = 1.12 \begin {gather*} \frac {\frac {4\,{\mathrm {e}}^2}{11}-\frac {12}{11}}{2\,{\mathrm {e}}^2-11\,x+38} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 17, normalized size = 1.06 \begin {gather*} - \frac {-12 + 4 e^{2}}{121 x - 418 - 22 e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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