Integrand size = 33, antiderivative size = 25 \[ \int \frac {e^{\frac {67837+6 x-3 x^2}{768 x}} \left (-67837-3 x^2\right )}{3072 x^2} \, dx=\frac {1}{4} e^{\frac {\frac {265}{3}-\frac {1}{256} (1-x)^2}{x}} \]
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Time = 0.11 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.92, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.061, Rules used = {12, 6838} \[ \int \frac {e^{\frac {67837+6 x-3 x^2}{768 x}} \left (-67837-3 x^2\right )}{3072 x^2} \, dx=\frac {1}{4} e^{\frac {-3 x^2+6 x+67837}{768 x}} \]
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Rule 12
Rule 6838
Rubi steps \begin{align*} \text {integral}& = \frac {\int \frac {e^{\frac {67837+6 x-3 x^2}{768 x}} \left (-67837-3 x^2\right )}{x^2} \, dx}{3072} \\ & = \frac {1}{4} e^{\frac {67837+6 x-3 x^2}{768 x}} \\ \end{align*}
Time = 0.08 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.88 \[ \int \frac {e^{\frac {67837+6 x-3 x^2}{768 x}} \left (-67837-3 x^2\right )}{3072 x^2} \, dx=\frac {1}{4} e^{\frac {1}{128}+\frac {67837}{768 x}-\frac {x}{256}} \]
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Time = 0.08 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.76
method | result | size |
gosper | \(\frac {{\mathrm e}^{-\frac {3 x^{2}-6 x -67837}{768 x}}}{4}\) | \(19\) |
norman | \(\frac {{\mathrm e}^{\frac {-3 x^{2}+6 x +67837}{768 x}}}{4}\) | \(19\) |
risch | \(\frac {{\mathrm e}^{-\frac {3 x^{2}-6 x -67837}{768 x}}}{4}\) | \(19\) |
parallelrisch | \(\frac {{\mathrm e}^{-\frac {3 x^{2}-6 x -67837}{768 x}}}{4}\) | \(19\) |
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none
Time = 0.22 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.72 \[ \int \frac {e^{\frac {67837+6 x-3 x^2}{768 x}} \left (-67837-3 x^2\right )}{3072 x^2} \, dx=\frac {1}{4} \, e^{\left (-\frac {3 \, x^{2} - 6 \, x - 67837}{768 \, x}\right )} \]
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Time = 0.07 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.60 \[ \int \frac {e^{\frac {67837+6 x-3 x^2}{768 x}} \left (-67837-3 x^2\right )}{3072 x^2} \, dx=\frac {e^{\frac {- \frac {x^{2}}{256} + \frac {x}{128} + \frac {67837}{768}}{x}}}{4} \]
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none
Time = 1.77 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.52 \[ \int \frac {e^{\frac {67837+6 x-3 x^2}{768 x}} \left (-67837-3 x^2\right )}{3072 x^2} \, dx=\frac {1}{4} \, e^{\left (-\frac {1}{256} \, x + \frac {67837}{768 \, x} + \frac {1}{128}\right )} \]
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Exception generated. \[ \int \frac {e^{\frac {67837+6 x-3 x^2}{768 x}} \left (-67837-3 x^2\right )}{3072 x^2} \, dx=\text {Exception raised: TypeError} \]
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Time = 12.14 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.52 \[ \int \frac {e^{\frac {67837+6 x-3 x^2}{768 x}} \left (-67837-3 x^2\right )}{3072 x^2} \, dx=\frac {{\mathrm {e}}^{\frac {67837}{768\,x}-\frac {x}{256}+\frac {1}{128}}}{4} \]
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