Integrand size = 45, antiderivative size = 24 \[ \int \frac {e^{\frac {49+126 x^2+81 x^4-9 x^5}{9 x^4}} \left (-196-252 x^2-9 x^5\right )}{9 x^5} \, dx=e^{-x+\frac {1}{9} \left (2+\frac {7 \left (\frac {1}{x}+x\right )}{x}\right )^2} \]
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Time = 0.24 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.79, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {12, 6820, 6838} \[ \int \frac {e^{\frac {49+126 x^2+81 x^4-9 x^5}{9 x^4}} \left (-196-252 x^2-9 x^5\right )}{9 x^5} \, dx=e^{\frac {49}{9 x^4}+\frac {14}{x^2}-x+9} \]
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Rule 12
Rule 6820
Rule 6838
Rubi steps \begin{align*} \text {integral}& = \frac {1}{9} \int \frac {e^{\frac {49+126 x^2+81 x^4-9 x^5}{9 x^4}} \left (-196-252 x^2-9 x^5\right )}{x^5} \, dx \\ & = \frac {1}{9} \int \frac {e^{9+\frac {49}{9 x^4}+\frac {14}{x^2}-x} \left (-196-252 x^2-9 x^5\right )}{x^5} \, dx \\ & = e^{9+\frac {49}{9 x^4}+\frac {14}{x^2}-x} \\ \end{align*}
Time = 0.06 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.79 \[ \int \frac {e^{\frac {49+126 x^2+81 x^4-9 x^5}{9 x^4}} \left (-196-252 x^2-9 x^5\right )}{9 x^5} \, dx=e^{9+\frac {49}{9 x^4}+\frac {14}{x^2}-x} \]
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Time = 0.11 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00
method | result | size |
gosper | \({\mathrm e}^{-\frac {9 x^{5}-81 x^{4}-126 x^{2}-49}{9 x^{4}}}\) | \(24\) |
norman | \({\mathrm e}^{\frac {-9 x^{5}+81 x^{4}+126 x^{2}+49}{9 x^{4}}}\) | \(24\) |
risch | \({\mathrm e}^{-\frac {9 x^{5}-81 x^{4}-126 x^{2}-49}{9 x^{4}}}\) | \(24\) |
parallelrisch | \({\mathrm e}^{-\frac {9 x^{5}-81 x^{4}-126 x^{2}-49}{9 x^{4}}}\) | \(24\) |
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Time = 0.25 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.96 \[ \int \frac {e^{\frac {49+126 x^2+81 x^4-9 x^5}{9 x^4}} \left (-196-252 x^2-9 x^5\right )}{9 x^5} \, dx=e^{\left (-\frac {9 \, x^{5} - 81 \, x^{4} - 126 \, x^{2} - 49}{9 \, x^{4}}\right )} \]
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Time = 0.07 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.83 \[ \int \frac {e^{\frac {49+126 x^2+81 x^4-9 x^5}{9 x^4}} \left (-196-252 x^2-9 x^5\right )}{9 x^5} \, dx=e^{\frac {- x^{5} + 9 x^{4} + 14 x^{2} + \frac {49}{9}}{x^{4}}} \]
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Time = 0.27 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.67 \[ \int \frac {e^{\frac {49+126 x^2+81 x^4-9 x^5}{9 x^4}} \left (-196-252 x^2-9 x^5\right )}{9 x^5} \, dx=e^{\left (-x + \frac {14}{x^{2}} + \frac {49}{9 \, x^{4}} + 9\right )} \]
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Time = 0.26 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.67 \[ \int \frac {e^{\frac {49+126 x^2+81 x^4-9 x^5}{9 x^4}} \left (-196-252 x^2-9 x^5\right )}{9 x^5} \, dx=e^{\left (-x + \frac {14}{x^{2}} + \frac {49}{9 \, x^{4}} + 9\right )} \]
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Time = 11.17 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.79 \[ \int \frac {e^{\frac {49+126 x^2+81 x^4-9 x^5}{9 x^4}} \left (-196-252 x^2-9 x^5\right )}{9 x^5} \, dx={\mathrm {e}}^{-x}\,{\mathrm {e}}^9\,{\mathrm {e}}^{\frac {14}{x^2}}\,{\mathrm {e}}^{\frac {49}{9\,x^4}} \]
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