Integrand size = 96, antiderivative size = 25 \[ \int \frac {-x^2+e^{\frac {729-9 x+2 x^2+x^3}{x}} \left (729-2 x^2-2 x^3\right )}{3 e^{\frac {2 \left (729-9 x+2 x^2+x^3\right )}{x}} x^2+6 e^{\frac {729-9 x+2 x^2+x^3}{x}} x^3+3 x^4} \, dx=\frac {1}{3 \left (e^{-\frac {9 (-81+x)}{x}+2 x+x^2}+x\right )} \]
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Time = 0.51 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.16, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {6820, 12, 6818} \[ \int \frac {-x^2+e^{\frac {729-9 x+2 x^2+x^3}{x}} \left (729-2 x^2-2 x^3\right )}{3 e^{\frac {2 \left (729-9 x+2 x^2+x^3\right )}{x}} x^2+6 e^{\frac {729-9 x+2 x^2+x^3}{x}} x^3+3 x^4} \, dx=\frac {e^9}{3 \left (e^{x^2+2 x+\frac {729}{x}}+e^9 x\right )} \]
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Rule 12
Rule 6818
Rule 6820
Rubi steps \begin{align*} \text {integral}& = \int \frac {e^9 \left (-e^9 x^2-e^{\frac {729}{x}+2 x+x^2} \left (-729+2 x^2+2 x^3\right )\right )}{3 x^2 \left (e^{\frac {729}{x}+2 x+x^2}+e^9 x\right )^2} \, dx \\ & = \frac {1}{3} e^9 \int \frac {-e^9 x^2-e^{\frac {729}{x}+2 x+x^2} \left (-729+2 x^2+2 x^3\right )}{x^2 \left (e^{\frac {729}{x}+2 x+x^2}+e^9 x\right )^2} \, dx \\ & = \frac {e^9}{3 \left (e^{\frac {729}{x}+2 x+x^2}+e^9 x\right )} \\ \end{align*}
Time = 0.06 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.16 \[ \int \frac {-x^2+e^{\frac {729-9 x+2 x^2+x^3}{x}} \left (729-2 x^2-2 x^3\right )}{3 e^{\frac {2 \left (729-9 x+2 x^2+x^3\right )}{x}} x^2+6 e^{\frac {729-9 x+2 x^2+x^3}{x}} x^3+3 x^4} \, dx=\frac {e^9}{3 \left (e^{\frac {729}{x}+2 x+x^2}+e^9 x\right )} \]
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Time = 1.06 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00
method | result | size |
norman | \(\frac {1}{3 x +3 \,{\mathrm e}^{\frac {x^{3}+2 x^{2}-9 x +729}{x}}}\) | \(25\) |
risch | \(\frac {1}{3 x +3 \,{\mathrm e}^{\frac {x^{3}+2 x^{2}-9 x +729}{x}}}\) | \(25\) |
parallelrisch | \(\frac {1}{3 x +3 \,{\mathrm e}^{\frac {x^{3}+2 x^{2}-9 x +729}{x}}}\) | \(25\) |
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Time = 0.24 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.96 \[ \int \frac {-x^2+e^{\frac {729-9 x+2 x^2+x^3}{x}} \left (729-2 x^2-2 x^3\right )}{3 e^{\frac {2 \left (729-9 x+2 x^2+x^3\right )}{x}} x^2+6 e^{\frac {729-9 x+2 x^2+x^3}{x}} x^3+3 x^4} \, dx=\frac {1}{3 \, {\left (x + e^{\left (\frac {x^{3} + 2 \, x^{2} - 9 \, x + 729}{x}\right )}\right )}} \]
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Time = 0.07 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.88 \[ \int \frac {-x^2+e^{\frac {729-9 x+2 x^2+x^3}{x}} \left (729-2 x^2-2 x^3\right )}{3 e^{\frac {2 \left (729-9 x+2 x^2+x^3\right )}{x}} x^2+6 e^{\frac {729-9 x+2 x^2+x^3}{x}} x^3+3 x^4} \, dx=\frac {1}{3 x + 3 e^{\frac {x^{3} + 2 x^{2} - 9 x + 729}{x}}} \]
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Time = 0.21 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.96 \[ \int \frac {-x^2+e^{\frac {729-9 x+2 x^2+x^3}{x}} \left (729-2 x^2-2 x^3\right )}{3 e^{\frac {2 \left (729-9 x+2 x^2+x^3\right )}{x}} x^2+6 e^{\frac {729-9 x+2 x^2+x^3}{x}} x^3+3 x^4} \, dx=\frac {e^{9}}{3 \, {\left (x e^{9} + e^{\left (x^{2} + 2 \, x + \frac {729}{x}\right )}\right )}} \]
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Time = 0.28 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.96 \[ \int \frac {-x^2+e^{\frac {729-9 x+2 x^2+x^3}{x}} \left (729-2 x^2-2 x^3\right )}{3 e^{\frac {2 \left (729-9 x+2 x^2+x^3\right )}{x}} x^2+6 e^{\frac {729-9 x+2 x^2+x^3}{x}} x^3+3 x^4} \, dx=\frac {1}{3 \, {\left (x + e^{\left (\frac {x^{3} + 2 \, x^{2} - 9 \, x + 729}{x}\right )}\right )}} \]
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Time = 7.81 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {-x^2+e^{\frac {729-9 x+2 x^2+x^3}{x}} \left (729-2 x^2-2 x^3\right )}{3 e^{\frac {2 \left (729-9 x+2 x^2+x^3\right )}{x}} x^2+6 e^{\frac {729-9 x+2 x^2+x^3}{x}} x^3+3 x^4} \, dx=\frac {{\mathrm {e}}^9}{3\,x\,{\mathrm {e}}^9+3\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{729/x}} \]
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