Integrand size = 21, antiderivative size = 26 \[ \int \frac {e^{-e^2} \left (-16+81 x^2\right )}{64 x^2} \, dx=\frac {1}{4} \left (5+\frac {e^{-e^2} \left (-1+\frac {9 x}{4}\right )^2}{x}\right ) \]
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Time = 0.01 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.04, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {12, 14} \[ \int \frac {e^{-e^2} \left (-16+81 x^2\right )}{64 x^2} \, dx=\frac {81}{64} e^{-e^2} x+\frac {e^{-e^2}}{4 x} \]
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Rule 12
Rule 14
Rubi steps \begin{align*} \text {integral}& = \frac {1}{64} e^{-e^2} \int \frac {-16+81 x^2}{x^2} \, dx \\ & = \frac {1}{64} e^{-e^2} \int \left (81-\frac {16}{x^2}\right ) \, dx \\ & = \frac {e^{-e^2}}{4 x}+\frac {81}{64} e^{-e^2} x \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.77 \[ \int \frac {e^{-e^2} \left (-16+81 x^2\right )}{64 x^2} \, dx=\frac {1}{64} e^{-e^2} \left (\frac {16}{x}+81 x\right ) \]
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Time = 0.11 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.65
method | result | size |
default | \(\frac {{\mathrm e}^{-{\mathrm e}^{2}} \left (81 x +\frac {16}{x}\right )}{64}\) | \(17\) |
gosper | \(\frac {{\mathrm e}^{-{\mathrm e}^{2}} \left (81 x^{2}+16\right )}{64 x}\) | \(18\) |
parallelrisch | \(\frac {{\mathrm e}^{-{\mathrm e}^{2}} \left (81 x^{2}+16\right )}{64 x}\) | \(18\) |
risch | \(\frac {81 x \,{\mathrm e}^{-{\mathrm e}^{2}}}{64}+\frac {{\mathrm e}^{-{\mathrm e}^{2}}}{4 x}\) | \(20\) |
norman | \(\frac {\frac {{\mathrm e}^{-{\mathrm e}^{2}}}{4}+\frac {81 \,{\mathrm e}^{-{\mathrm e}^{2}} x^{2}}{64}}{x}\) | \(23\) |
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Time = 0.27 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.65 \[ \int \frac {e^{-e^2} \left (-16+81 x^2\right )}{64 x^2} \, dx=\frac {{\left (81 \, x^{2} + 16\right )} e^{\left (-e^{2}\right )}}{64 \, x} \]
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Time = 0.03 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.46 \[ \int \frac {e^{-e^2} \left (-16+81 x^2\right )}{64 x^2} \, dx=\frac {81 x + \frac {16}{x}}{64 e^{e^{2}}} \]
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Time = 0.20 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.62 \[ \int \frac {e^{-e^2} \left (-16+81 x^2\right )}{64 x^2} \, dx=\frac {1}{64} \, {\left (81 \, x + \frac {16}{x}\right )} e^{\left (-e^{2}\right )} \]
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Time = 0.26 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.62 \[ \int \frac {e^{-e^2} \left (-16+81 x^2\right )}{64 x^2} \, dx=\frac {1}{64} \, {\left (81 \, x + \frac {16}{x}\right )} e^{\left (-e^{2}\right )} \]
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Time = 0.05 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.65 \[ \int \frac {e^{-e^2} \left (-16+81 x^2\right )}{64 x^2} \, dx=\frac {{\mathrm {e}}^{-{\mathrm {e}}^2}\,\left (81\,x^2+16\right )}{64\,x} \]
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