Optimal. Leaf size=20 \[ \frac {4}{e^8-3 \left (4+\frac {x}{2}\right )+29 x} \]
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Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 0.85, number of steps used = 4, number of rules used = 4, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 1981, 27, 32} \begin {gather*} -\frac {8}{2 \left (12-e^8\right )-55 x} \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 (440 \int \frac {1}{576+4 e^{16}-2640 x+3025 x^2+e^8 (-96+220 x)} \, dx\right )\\ &=-\left (440 \int \frac {1}{4 \left (12-e^8\right )^2-220 \left (12-e^8\right ) x+3025 x^2} \, dx\right )\\ &=-\left (440 \int \frac {1}{\left (-24+2 e^8+55 x\right )^2} \, dx\right )\\ &=-\frac {8}{2 \left (12-e^8\right )-55 x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 0.70 \begin {gather*} \frac {8}{-24+2 e^8+55 x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 13, normalized size = 0.65 \begin {gather*} \frac {8}{55 \, x + 2 \, e^{8} - 24} \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 = 0.18, size = 12, normalized size = 0.60
method | result | size |
risch | \(\frac {4}{\frac {55 x}{2}+{\mathrm e}^{8}-12}\) | \(12\) |
gosper | \(\frac {8}{2 \,{\mathrm e}^{8}+55 x -24}\) | \(14\) |
norman | \(\frac {8}{2 \,{\mathrm e}^{8}+55 x -24}\) | \(14\) |
meijerg | \(-\frac {4 x}{\left (\frac {2 \,{\mathrm e}^{8}}{55}-\frac {24}{55}\right ) \left ({\mathrm e}^{8}-12\right ) \left (1+\frac {55 x}{2 \left ({\mathrm e}^{8}-12\right )}\right )}\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 13, normalized size = 0.65 \begin {gather*} \frac {8}{55 \, x + 2 \, e^{8} - 24} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.24, size = 13, normalized size = 0.65 \begin {gather*} \frac {8}{55\,x+2\,{\mathrm {e}}^8-24} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 10, normalized size = 0.50 \begin {gather*} \frac {440}{3025 x - 1320 + 110 e^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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