Integrand size = 47, antiderivative size = 20 \[ \int \frac {e^{\frac {125+50 x+5 x^2+153 x^6+x^7}{5 x^6}} \left (-750-250 x-20 x^2+x^7\right )}{5 x^7} \, dx=e^{30+\frac {3+x}{5}+\frac {(5+x)^2}{x^6}} \]
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Time = 0.19 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.35, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {12, 6838} \[ \int \frac {e^{\frac {125+50 x+5 x^2+153 x^6+x^7}{5 x^6}} \left (-750-250 x-20 x^2+x^7\right )}{5 x^7} \, dx=e^{\frac {x^7+153 x^6+5 x^2+50 x+125}{5 x^6}} \]
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Rule 12
Rule 6838
Rubi steps \begin{align*} \text {integral}& = \frac {1}{5} \int \frac {e^{\frac {125+50 x+5 x^2+153 x^6+x^7}{5 x^6}} \left (-750-250 x-20 x^2+x^7\right )}{x^7} \, dx \\ & = e^{\frac {125+50 x+5 x^2+153 x^6+x^7}{5 x^6}} \\ \end{align*}
Time = 0.09 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.20 \[ \int \frac {e^{\frac {125+50 x+5 x^2+153 x^6+x^7}{5 x^6}} \left (-750-250 x-20 x^2+x^7\right )}{5 x^7} \, dx=e^{\frac {153}{5}+\frac {25}{x^6}+\frac {10}{x^5}+\frac {1}{x^4}+\frac {x}{5}} \]
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Time = 0.12 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.25
method | result | size |
gosper | \({\mathrm e}^{\frac {x^{7}+153 x^{6}+5 x^{2}+50 x +125}{5 x^{6}}}\) | \(25\) |
derivativedivides | \({\mathrm e}^{\frac {x^{7}+153 x^{6}+5 x^{2}+50 x +125}{5 x^{6}}}\) | \(25\) |
default | \({\mathrm e}^{\frac {x^{7}+153 x^{6}+5 x^{2}+50 x +125}{5 x^{6}}}\) | \(25\) |
norman | \({\mathrm e}^{\frac {x^{7}+153 x^{6}+5 x^{2}+50 x +125}{5 x^{6}}}\) | \(25\) |
risch | \({\mathrm e}^{\frac {x^{7}+153 x^{6}+5 x^{2}+50 x +125}{5 x^{6}}}\) | \(25\) |
parallelrisch | \({\mathrm e}^{\frac {x^{7}+153 x^{6}+5 x^{2}+50 x +125}{5 x^{6}}}\) | \(25\) |
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none
Time = 0.24 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.20 \[ \int \frac {e^{\frac {125+50 x+5 x^2+153 x^6+x^7}{5 x^6}} \left (-750-250 x-20 x^2+x^7\right )}{5 x^7} \, dx=e^{\left (\frac {x^{7} + 153 \, x^{6} + 5 \, x^{2} + 50 \, x + 125}{5 \, x^{6}}\right )} \]
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Time = 0.08 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.20 \[ \int \frac {e^{\frac {125+50 x+5 x^2+153 x^6+x^7}{5 x^6}} \left (-750-250 x-20 x^2+x^7\right )}{5 x^7} \, dx=e^{\frac {\frac {x^{7}}{5} + \frac {153 x^{6}}{5} + x^{2} + 10 x + 25}{x^{6}}} \]
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none
Time = 0.28 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int \frac {e^{\frac {125+50 x+5 x^2+153 x^6+x^7}{5 x^6}} \left (-750-250 x-20 x^2+x^7\right )}{5 x^7} \, dx=e^{\left (\frac {1}{5} \, x + \frac {1}{x^{4}} + \frac {10}{x^{5}} + \frac {25}{x^{6}} + \frac {153}{5}\right )} \]
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Time = 0.26 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int \frac {e^{\frac {125+50 x+5 x^2+153 x^6+x^7}{5 x^6}} \left (-750-250 x-20 x^2+x^7\right )}{5 x^7} \, dx=e^{\left (\frac {1}{5} \, x + \frac {1}{x^{4}} + \frac {10}{x^{5}} + \frac {25}{x^{6}} + \frac {153}{5}\right )} \]
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Time = 10.48 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.15 \[ \int \frac {e^{\frac {125+50 x+5 x^2+153 x^6+x^7}{5 x^6}} \left (-750-250 x-20 x^2+x^7\right )}{5 x^7} \, dx={\mathrm {e}}^{x/5}\,{\mathrm {e}}^{\frac {1}{x^4}}\,{\mathrm {e}}^{153/5}\,{\mathrm {e}}^{\frac {10}{x^5}}\,{\mathrm {e}}^{\frac {25}{x^6}} \]
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