Integrand size = 48, antiderivative size = 25 \[ \int \frac {e^{\frac {225+9 x+45 e^{5+x} x-5 x^2}{5 x}} \left (-45-x^2+9 e^{5+x} x^2\right )}{x^2} \, dx=e^{-x+\frac {9 \left (5+\frac {x}{5}+e^{5+x} x\right )}{x}} \]
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Time = 0.28 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.021, Rules used = {6838} \[ \int \frac {e^{\frac {225+9 x+45 e^{5+x} x-5 x^2}{5 x}} \left (-45-x^2+9 e^{5+x} x^2\right )}{x^2} \, dx=e^{\frac {-5 x^2+45 e^{x+5} x+9 x+225}{5 x}} \]
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Rule 6838
Rubi steps \begin{align*} \text {integral}& = e^{\frac {225+9 x+45 e^{5+x} x-5 x^2}{5 x}} \\ \end{align*}
Time = 0.26 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.84 \[ \int \frac {e^{\frac {225+9 x+45 e^{5+x} x-5 x^2}{5 x}} \left (-45-x^2+9 e^{5+x} x^2\right )}{x^2} \, dx=e^{\frac {9}{5}+9 e^{5+x}+\frac {45}{x}-x} \]
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Time = 0.19 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.96
method | result | size |
derivativedivides | \({\mathrm e}^{\frac {45 x \,{\mathrm e}^{5+x}-5 x^{2}+9 x +225}{5 x}}\) | \(24\) |
default | \({\mathrm e}^{\frac {45 x \,{\mathrm e}^{5+x}-5 x^{2}+9 x +225}{5 x}}\) | \(24\) |
norman | \({\mathrm e}^{\frac {45 x \,{\mathrm e}^{5+x}-5 x^{2}+9 x +225}{5 x}}\) | \(24\) |
risch | \({\mathrm e}^{-\frac {-45 x \,{\mathrm e}^{5+x}+5 x^{2}-9 x -225}{5 x}}\) | \(24\) |
parallelrisch | \({\mathrm e}^{\frac {45 x \,{\mathrm e}^{5+x}-5 x^{2}+9 x +225}{5 x}}\) | \(24\) |
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none
Time = 0.25 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.92 \[ \int \frac {e^{\frac {225+9 x+45 e^{5+x} x-5 x^2}{5 x}} \left (-45-x^2+9 e^{5+x} x^2\right )}{x^2} \, dx=e^{\left (-\frac {5 \, x^{2} - 45 \, x e^{\left (x + 5\right )} - 9 \, x - 225}{5 \, x}\right )} \]
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Time = 0.15 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.80 \[ \int \frac {e^{\frac {225+9 x+45 e^{5+x} x-5 x^2}{5 x}} \left (-45-x^2+9 e^{5+x} x^2\right )}{x^2} \, dx=e^{\frac {- x^{2} + 9 x e^{x + 5} + \frac {9 x}{5} + 45}{x}} \]
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none
Time = 0.28 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.68 \[ \int \frac {e^{\frac {225+9 x+45 e^{5+x} x-5 x^2}{5 x}} \left (-45-x^2+9 e^{5+x} x^2\right )}{x^2} \, dx=e^{\left (-x + \frac {45}{x} + 9 \, e^{\left (x + 5\right )} + \frac {9}{5}\right )} \]
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none
Time = 0.27 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.68 \[ \int \frac {e^{\frac {225+9 x+45 e^{5+x} x-5 x^2}{5 x}} \left (-45-x^2+9 e^{5+x} x^2\right )}{x^2} \, dx=e^{\left (-x + \frac {45}{x} + 9 \, e^{\left (x + 5\right )} + \frac {9}{5}\right )} \]
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Time = 13.82 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.80 \[ \int \frac {e^{\frac {225+9 x+45 e^{5+x} x-5 x^2}{5 x}} \left (-45-x^2+9 e^{5+x} x^2\right )}{x^2} \, dx={\mathrm {e}}^{9\,{\mathrm {e}}^5\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{9/5}\,{\mathrm {e}}^{45/x} \]
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