Integrand size = 30, antiderivative size = 20 \[ \int e^{-e-e^x+x+x^2} \left (1-e^x+2 x\right ) \log ^2(25) \, dx=e^{-e-e^x+x+x^2} \log ^2(25) \]
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Time = 0.06 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {12, 6838} \[ \int e^{-e-e^x+x+x^2} \left (1-e^x+2 x\right ) \log ^2(25) \, dx=e^{x^2+x-e^x-e} \log ^2(25) \]
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Rule 12
Rule 6838
Rubi steps \begin{align*} \text {integral}& = \log ^2(25) \int e^{-e-e^x+x+x^2} \left (1-e^x+2 x\right ) \, dx \\ & = e^{-e-e^x+x+x^2} \log ^2(25) \\ \end{align*}
Time = 0.19 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int e^{-e-e^x+x+x^2} \left (1-e^x+2 x\right ) \log ^2(25) \, dx=e^{-e-e^x+x+x^2} \log ^2(25) \]
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Time = 0.10 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.05
method | result | size |
risch | \(4 \ln \left (5\right )^{2} {\mathrm e}^{-{\mathrm e}^{x}-{\mathrm e}+x^{2}+x}\) | \(21\) |
derivativedivides | \({\mathrm e}^{\ln \left (4 \ln \left (5\right )^{2}\right )-{\mathrm e}^{x}-{\mathrm e}+x^{2}+x}\) | \(22\) |
default | \({\mathrm e}^{\ln \left (4 \ln \left (5\right )^{2}\right )-{\mathrm e}^{x}-{\mathrm e}+x^{2}+x}\) | \(22\) |
norman | \({\mathrm e}^{\ln \left (4 \ln \left (5\right )^{2}\right )-{\mathrm e}^{x}-{\mathrm e}+x^{2}+x}\) | \(22\) |
parallelrisch | \({\mathrm e}^{\ln \left (4 \ln \left (5\right )^{2}\right )-{\mathrm e}^{x}-{\mathrm e}+x^{2}+x}\) | \(22\) |
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none
Time = 0.27 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.05 \[ \int e^{-e-e^x+x+x^2} \left (1-e^x+2 x\right ) \log ^2(25) \, dx=e^{\left (x^{2} + x - e - e^{x} + \log \left (4 \, \log \left (5\right )^{2}\right )\right )} \]
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Time = 0.09 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int e^{-e-e^x+x+x^2} \left (1-e^x+2 x\right ) \log ^2(25) \, dx=4 e^{x^{2} + x - e^{x} - e} \log {\left (5 \right )}^{2} \]
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none
Time = 0.17 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int e^{-e-e^x+x+x^2} \left (1-e^x+2 x\right ) \log ^2(25) \, dx=4 \, e^{\left (x^{2} + x - e - e^{x}\right )} \log \left (5\right )^{2} \]
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none
Time = 0.26 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.05 \[ \int e^{-e-e^x+x+x^2} \left (1-e^x+2 x\right ) \log ^2(25) \, dx=e^{\left (x^{2} + x - e - e^{x} + \log \left (4 \, \log \left (5\right )^{2}\right )\right )} \]
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Time = 0.09 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int e^{-e-e^x+x+x^2} \left (1-e^x+2 x\right ) \log ^2(25) \, dx=4\,{\mathrm {e}}^{-\mathrm {e}}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-{\mathrm {e}}^x}\,{\mathrm {e}}^x\,{\ln \left (5\right )}^2 \]
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