Integrand size = 70, antiderivative size = 25 \[ \int \frac {e^{-x/9} \left (4 e^{x/9} x^2+e^{\frac {e^{-x/9} \left (e^{x/9} (-81-x)+45 x\right )}{x}} \left (324 e^{x/9}-20 x^2\right )\right )}{x^2} \, dx=4 \left (e^{\frac {-81-x+45 e^{-x/9} x}{x}}+x\right ) \]
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\[ \int \frac {e^{-x/9} \left (4 e^{x/9} x^2+e^{\frac {e^{-x/9} \left (e^{x/9} (-81-x)+45 x\right )}{x}} \left (324 e^{x/9}-20 x^2\right )\right )}{x^2} \, dx=\int \frac {e^{-x/9} \left (4 e^{x/9} x^2+e^{\frac {e^{-x/9} \left (e^{x/9} (-81-x)+45 x\right )}{x}} \left (324 e^{x/9}-20 x^2\right )\right )}{x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \left (4-20 e^{-1+45 e^{-x/9}-\frac {81}{x}-\frac {x}{9}}+\frac {324 e^{-1+45 e^{-x/9}-\frac {81}{x}}}{x^2}\right ) \, dx \\ & = 4 x-20 \int e^{-1+45 e^{-x/9}-\frac {81}{x}-\frac {x}{9}} \, dx+324 \int \frac {e^{-1+45 e^{-x/9}-\frac {81}{x}}}{x^2} \, dx \\ \end{align*}
Time = 0.94 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.96 \[ \int \frac {e^{-x/9} \left (4 e^{x/9} x^2+e^{\frac {e^{-x/9} \left (e^{x/9} (-81-x)+45 x\right )}{x}} \left (324 e^{x/9}-20 x^2\right )\right )}{x^2} \, dx=4 e^{-1+45 e^{-x/9}-\frac {81}{x}}+4 x \]
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Time = 0.56 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.28
method | result | size |
parallelrisch | \(4 x +4 \,{\mathrm e}^{\frac {\left (\left (-x -81\right ) {\mathrm e}^{\frac {x}{9}}+45 x \right ) {\mathrm e}^{-\frac {x}{9}}}{x}}\) | \(32\) |
parts | \(4 x +4 \,{\mathrm e}^{\frac {\left (\left (-x -81\right ) {\mathrm e}^{\frac {x}{9}}+45 x \right ) {\mathrm e}^{-\frac {x}{9}}}{x}}\) | \(32\) |
risch | \(4 x +4 \,{\mathrm e}^{-\frac {\left (x \,{\mathrm e}^{\frac {x}{9}}+81 \,{\mathrm e}^{\frac {x}{9}}-45 x \right ) {\mathrm e}^{-\frac {x}{9}}}{x}}\) | \(33\) |
norman | \(\frac {\left (4 x^{2} {\mathrm e}^{\frac {x}{9}}+4 x \,{\mathrm e}^{\frac {x}{9}} {\mathrm e}^{\frac {\left (\left (-x -81\right ) {\mathrm e}^{\frac {x}{9}}+45 x \right ) {\mathrm e}^{-\frac {x}{9}}}{x}}\right ) {\mathrm e}^{-\frac {x}{9}}}{x}\) | \(53\) |
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Time = 0.25 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.12 \[ \int \frac {e^{-x/9} \left (4 e^{x/9} x^2+e^{\frac {e^{-x/9} \left (e^{x/9} (-81-x)+45 x\right )}{x}} \left (324 e^{x/9}-20 x^2\right )\right )}{x^2} \, dx=4 \, x + 4 \, e^{\left (-\frac {{\left ({\left (x + 81\right )} e^{\left (\frac {1}{9} \, x\right )} - 45 \, x\right )} e^{\left (-\frac {1}{9} \, x\right )}}{x}\right )} \]
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Time = 0.12 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.04 \[ \int \frac {e^{-x/9} \left (4 e^{x/9} x^2+e^{\frac {e^{-x/9} \left (e^{x/9} (-81-x)+45 x\right )}{x}} \left (324 e^{x/9}-20 x^2\right )\right )}{x^2} \, dx=4 x + 4 e^{\frac {\left (45 x + \left (- x - 81\right ) e^{\frac {x}{9}}\right ) e^{- \frac {x}{9}}}{x}} \]
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Time = 0.29 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.80 \[ \int \frac {e^{-x/9} \left (4 e^{x/9} x^2+e^{\frac {e^{-x/9} \left (e^{x/9} (-81-x)+45 x\right )}{x}} \left (324 e^{x/9}-20 x^2\right )\right )}{x^2} \, dx=4 \, x + 4 \, e^{\left (-\frac {81}{x} + 45 \, e^{\left (-\frac {1}{9} \, x\right )} - 1\right )} \]
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Time = 0.39 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.80 \[ \int \frac {e^{-x/9} \left (4 e^{x/9} x^2+e^{\frac {e^{-x/9} \left (e^{x/9} (-81-x)+45 x\right )}{x}} \left (324 e^{x/9}-20 x^2\right )\right )}{x^2} \, dx=4 \, x + 4 \, e^{\left (-\frac {81}{x} + 45 \, e^{\left (-\frac {1}{9} \, x\right )} - 1\right )} \]
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Time = 13.42 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.84 \[ \int \frac {e^{-x/9} \left (4 e^{x/9} x^2+e^{\frac {e^{-x/9} \left (e^{x/9} (-81-x)+45 x\right )}{x}} \left (324 e^{x/9}-20 x^2\right )\right )}{x^2} \, dx=4\,x+4\,{\mathrm {e}}^{\frac {45}{{\left ({\mathrm {e}}^x\right )}^{1/9}}}\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{-\frac {81}{x}} \]
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