Integrand size = 14, antiderivative size = 9 \[ \int 1125 e^{-2+225 x^5} x^4 \, dx=e^{-2+225 x^5} \]
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Time = 0.01 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 2240} \[ \int 1125 e^{-2+225 x^5} x^4 \, dx=e^{225 x^5-2} \]
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Rule 12
Rule 2240
Rubi steps \begin{align*} \text {integral}& = 1125 \int e^{-2+225 x^5} x^4 \, dx \\ & = e^{-2+225 x^5} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int 1125 e^{-2+225 x^5} x^4 \, dx=e^{-2+225 x^5} \]
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Time = 0.06 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00
method | result | size |
gosper | \({\mathrm e}^{225 x^{5}-2}\) | \(9\) |
derivativedivides | \({\mathrm e}^{225 x^{5}-2}\) | \(9\) |
default | \({\mathrm e}^{225 x^{5}-2}\) | \(9\) |
norman | \({\mathrm e}^{225 x^{5}-2}\) | \(9\) |
risch | \({\mathrm e}^{225 x^{5}-2}\) | \(9\) |
parallelrisch | \({\mathrm e}^{225 x^{5}-2}\) | \(9\) |
meijerg | \(-{\mathrm e}^{-2} \left (1-{\mathrm e}^{225 x^{5}}\right )\) | \(15\) |
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none
Time = 0.25 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.89 \[ \int 1125 e^{-2+225 x^5} x^4 \, dx=e^{\left (225 \, x^{5} - 2\right )} \]
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Time = 0.04 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int 1125 e^{-2+225 x^5} x^4 \, dx=e^{225 x^{5} - 2} \]
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none
Time = 0.20 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.89 \[ \int 1125 e^{-2+225 x^5} x^4 \, dx=e^{\left (225 \, x^{5} - 2\right )} \]
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none
Time = 0.26 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.89 \[ \int 1125 e^{-2+225 x^5} x^4 \, dx=e^{\left (225 \, x^{5} - 2\right )} \]
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Time = 8.49 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int 1125 e^{-2+225 x^5} x^4 \, dx={\mathrm {e}}^{-2}\,{\mathrm {e}}^{225\,x^5} \]
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