Integrand size = 28, antiderivative size = 20 \[ \int -\frac {440}{576+4 e^{16}-2640 x+3025 x^2+e^8 (-96+220 x)} \, dx=\frac {4}{e^8-3 \left (4+\frac {x}{2}\right )+29 x} \]
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Time = 0.01 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 2006, 27, 32} \[ \int -\frac {440}{576+4 e^{16}-2640 x+3025 x^2+e^8 (-96+220 x)} \, dx=-\frac {8}{2 \left (12-e^8\right )-55 x} \]
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Rule 12
Rule 27
Rule 32
Rule 2006
Rubi steps \begin{align*} \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{align*}
Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.70 \[ \int -\frac {440}{576+4 e^{16}-2640 x+3025 x^2+e^8 (-96+220 x)} \, dx=\frac {8}{-24+2 e^8+55 x} \]
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Time = 0.48 (sec) , antiderivative size = 12, normalized size of antiderivative = 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 | \(\frac {8}{2 \,{\mathrm e}^{8}+55 x -24}\) | \(14\) |
parallelrisch | \(\frac {8}{2 \,{\mathrm e}^{8}+55 x -24}\) | \(14\) |
meijerg | \(-\frac {4 x}{\left (\frac {2 \,{\mathrm e}^{8}}{55}-\frac {24}{55}\right ) \left ({\mathrm e}^{8}-12\right ) \left (1+\frac {55 x}{2 \left ({\mathrm e}^{8}-12\right )}\right )}\) | \(31\) |
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Time = 0.23 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.65 \[ \int -\frac {440}{576+4 e^{16}-2640 x+3025 x^2+e^8 (-96+220 x)} \, dx=\frac {8}{55 \, x + 2 \, e^{8} - 24} \]
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Time = 0.09 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.50 \[ \int -\frac {440}{576+4 e^{16}-2640 x+3025 x^2+e^8 (-96+220 x)} \, dx=\frac {440}{3025 x - 1320 + 110 e^{8}} \]
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Time = 0.19 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.65 \[ \int -\frac {440}{576+4 e^{16}-2640 x+3025 x^2+e^8 (-96+220 x)} \, dx=\frac {8}{55 \, x + 2 \, e^{8} - 24} \]
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Time = 0.27 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.65 \[ \int -\frac {440}{576+4 e^{16}-2640 x+3025 x^2+e^8 (-96+220 x)} \, dx=\frac {8}{55 \, x + 2 \, e^{8} - 24} \]
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Time = 11.45 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.65 \[ \int -\frac {440}{576+4 e^{16}-2640 x+3025 x^2+e^8 (-96+220 x)} \, dx=\frac {8}{55\,x+2\,{\mathrm {e}}^8-24} \]
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