Integrand size = 26, antiderivative size = 16 \[ \int -\frac {e^3 (1-80 x)}{16 x \left (-x+80 x^2\right )} \, dx=2-e^3 \left (-5+\frac {1}{16 x}\right ) \]
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Time = 0.01 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.62, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12, 777} \[ \int -\frac {e^3 (1-80 x)}{16 x \left (-x+80 x^2\right )} \, dx=-\frac {e^3}{16 x} \]
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Rule 12
Rule 777
Rubi steps \begin{align*} \text {integral}& = -\left (\frac {1}{16} e^3 \int \frac {1-80 x}{x \left (-x+80 x^2\right )} \, dx\right ) \\ & = -\frac {e^3}{16 x} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.62 \[ \int -\frac {e^3 (1-80 x)}{16 x \left (-x+80 x^2\right )} \, dx=-\frac {e^3}{16 x} \]
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Time = 0.44 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.50
method | result | size |
norman | \(-\frac {{\mathrm e}^{3}}{16 x}\) | \(8\) |
risch | \(-\frac {{\mathrm e}^{3}}{16 x}\) | \(8\) |
gosper | \(\frac {{\mathrm e}^{\ln \left (-\frac {80 x -1}{16 x}\right )+3}}{80 x -1}\) | \(23\) |
default | \(\frac {{\mathrm e}^{\ln \left (-\frac {80 x -1}{16 x}\right )+3}}{80 x -1}\) | \(23\) |
parallelrisch | \(\frac {{\mathrm e}^{\ln \left (-\frac {80 x -1}{16 x}\right )+3}}{80 x -1}\) | \(23\) |
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none
Time = 0.23 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.44 \[ \int -\frac {e^3 (1-80 x)}{16 x \left (-x+80 x^2\right )} \, dx=-\frac {e^{3}}{16 \, x} \]
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Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.44 \[ \int -\frac {e^3 (1-80 x)}{16 x \left (-x+80 x^2\right )} \, dx=- \frac {e^{3}}{16 x} \]
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none
Time = 0.20 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.44 \[ \int -\frac {e^3 (1-80 x)}{16 x \left (-x+80 x^2\right )} \, dx=-\frac {e^{3}}{16 \, x} \]
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none
Time = 0.25 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.44 \[ \int -\frac {e^3 (1-80 x)}{16 x \left (-x+80 x^2\right )} \, dx=-\frac {e^{3}}{16 \, x} \]
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Time = 0.06 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.44 \[ \int -\frac {e^3 (1-80 x)}{16 x \left (-x+80 x^2\right )} \, dx=-\frac {{\mathrm {e}}^3}{16\,x} \]
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