Integrand size = 44, antiderivative size = 19 \[ \int e^{25+5 x+5 x^2-\frac {e^x x^2}{2}} \left (5+10 x+\frac {1}{2} e^x \left (-2 x-x^2\right )\right ) \, dx=e^{25+x \left (5+5 x-\frac {e^x x}{2}\right )} \]
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Time = 0.10 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.16, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.023, Rules used = {6838} \[ \int e^{25+5 x+5 x^2-\frac {e^x x^2}{2}} \left (5+10 x+\frac {1}{2} e^x \left (-2 x-x^2\right )\right ) \, dx=e^{-\frac {1}{2} e^x x^2+5 x^2+5 x+25} \]
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Rule 6838
Rubi steps \begin{align*} \text {integral}& = e^{25+5 x+5 x^2-\frac {e^x x^2}{2}} \\ \end{align*}
Time = 0.46 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.16 \[ \int e^{25+5 x+5 x^2-\frac {e^x x^2}{2}} \left (5+10 x+\frac {1}{2} e^x \left (-2 x-x^2\right )\right ) \, dx=e^{25+5 x+5 x^2-\frac {e^x x^2}{2}} \]
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Time = 0.15 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00
method | result | size |
risch | \({\mathrm e}^{-\frac {{\mathrm e}^{x} x^{2}}{2}+5 x^{2}+5 x +25}\) | \(19\) |
norman | \({\mathrm e}^{-x^{2} {\mathrm e}^{x -\ln \left (2\right )}+5 x^{2}+5 x +25}\) | \(24\) |
parallelrisch | \({\mathrm e}^{-x^{2} {\mathrm e}^{x -\ln \left (2\right )}+5 x^{2}+5 x +25}\) | \(24\) |
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Time = 0.24 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.21 \[ \int e^{25+5 x+5 x^2-\frac {e^x x^2}{2}} \left (5+10 x+\frac {1}{2} e^x \left (-2 x-x^2\right )\right ) \, dx=e^{\left (-x^{2} e^{\left (x - \log \left (2\right )\right )} + 5 \, x^{2} + 5 \, x + 25\right )} \]
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Time = 0.10 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00 \[ \int e^{25+5 x+5 x^2-\frac {e^x x^2}{2}} \left (5+10 x+\frac {1}{2} e^x \left (-2 x-x^2\right )\right ) \, dx=e^{- \frac {x^{2} e^{x}}{2} + 5 x^{2} + 5 x + 25} \]
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Time = 0.26 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95 \[ \int e^{25+5 x+5 x^2-\frac {e^x x^2}{2}} \left (5+10 x+\frac {1}{2} e^x \left (-2 x-x^2\right )\right ) \, dx=e^{\left (-\frac {1}{2} \, x^{2} e^{x} + 5 \, x^{2} + 5 \, x + 25\right )} \]
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Time = 0.29 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.21 \[ \int e^{25+5 x+5 x^2-\frac {e^x x^2}{2}} \left (5+10 x+\frac {1}{2} e^x \left (-2 x-x^2\right )\right ) \, dx=e^{\left (-x^{2} e^{\left (x - \log \left (2\right )\right )} + 5 \, x^{2} + 5 \, x + 25\right )} \]
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Time = 0.14 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.11 \[ \int e^{25+5 x+5 x^2-\frac {e^x x^2}{2}} \left (5+10 x+\frac {1}{2} e^x \left (-2 x-x^2\right )\right ) \, dx={\mathrm {e}}^{5\,x}\,{\mathrm {e}}^{25}\,{\mathrm {e}}^{-\frac {x^2\,{\mathrm {e}}^x}{2}}\,{\mathrm {e}}^{5\,x^2} \]
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