Integrand size = 18, antiderivative size = 12 \[ \int -\frac {2400 e^{\frac {400-20 x^6}{x^6}}}{x^7} \, dx=e^{-20+\frac {400}{x^6}}+\log (25) \]
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Time = 0.04 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 2257, 2240} \[ \int -\frac {2400 e^{\frac {400-20 x^6}{x^6}}}{x^7} \, dx=e^{\frac {400}{x^6}-20} \]
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Rule 12
Rule 2240
Rule 2257
Rubi steps \begin{align*} \text {integral}& = -\left (2400 \int \frac {e^{\frac {400-20 x^6}{x^6}}}{x^7} \, dx\right ) \\ & = -\left (2400 \int \frac {e^{-20+\frac {400}{x^6}}}{x^7} \, dx\right ) \\ & = e^{-20+\frac {400}{x^6}} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75 \[ \int -\frac {2400 e^{\frac {400-20 x^6}{x^6}}}{x^7} \, dx=e^{-20+\frac {400}{x^6}} \]
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Time = 0.06 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00
method | result | size |
gosper | \({\mathrm e}^{-\frac {20 \left (x^{6}-20\right )}{x^{6}}}\) | \(12\) |
risch | \({\mathrm e}^{-\frac {20 \left (x^{6}-20\right )}{x^{6}}}\) | \(12\) |
parallelrisch | \({\mathrm e}^{-\frac {20 \left (x^{6}-20\right )}{x^{6}}}\) | \(12\) |
derivativedivides | \({\mathrm e}^{\frac {-20 x^{6}+400}{x^{6}}}\) | \(13\) |
default | \({\mathrm e}^{\frac {-20 x^{6}+400}{x^{6}}}\) | \(13\) |
norman | \({\mathrm e}^{\frac {-20 x^{6}+400}{x^{6}}}\) | \(13\) |
meijerg | \(-{\mathrm e}^{-20} \left (1-{\mathrm e}^{\frac {400}{x^{6}}}\right )\) | \(15\) |
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Time = 0.22 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92 \[ \int -\frac {2400 e^{\frac {400-20 x^6}{x^6}}}{x^7} \, dx=e^{\left (-\frac {20 \, {\left (x^{6} - 20\right )}}{x^{6}}\right )} \]
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Time = 0.05 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int -\frac {2400 e^{\frac {400-20 x^6}{x^6}}}{x^7} \, dx=e^{\frac {400 - 20 x^{6}}{x^{6}}} \]
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Time = 0.18 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int -\frac {2400 e^{\frac {400-20 x^6}{x^6}}}{x^7} \, dx=e^{\left (\frac {400}{x^{6}} - 20\right )} \]
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Time = 0.26 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int -\frac {2400 e^{\frac {400-20 x^6}{x^6}}}{x^7} \, dx=e^{\left (\frac {400}{x^{6}} - 20\right )} \]
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Time = 8.50 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75 \[ \int -\frac {2400 e^{\frac {400-20 x^6}{x^6}}}{x^7} \, dx={\mathrm {e}}^{-20}\,{\mathrm {e}}^{\frac {400}{x^6}} \]
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