Integrand size = 52, antiderivative size = 30 \[ \int \frac {e^{3/x} (-3+x)-17 x+6 x^2+e^x \left (-12 x-12 x^2\right )+e^{2 x} \left (-2 x-4 x^2\right )}{x} \, dx=-\left (\left (-1-e^{3/x}+2 \left (\left (3+e^x\right )^2-x\right )-x\right ) x\right ) \]
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Time = 0.07 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.60, number of steps used = 9, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {14, 2207, 2225, 2326} \[ \int \frac {e^{3/x} (-3+x)-17 x+6 x^2+e^x \left (-12 x-12 x^2\right )+e^{2 x} \left (-2 x-4 x^2\right )}{x} \, dx=3 x^2+e^{3/x} x-17 x+12 e^x+e^{2 x}-12 e^x (x+1)-e^{2 x} (2 x+1) \]
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Rule 14
Rule 2207
Rule 2225
Rule 2326
Rubi steps \begin{align*} \text {integral}& = \int \left (-12 e^x (1+x)-2 e^{2 x} (1+2 x)+\frac {-3 e^{3/x}-17 x+e^{3/x} x+6 x^2}{x}\right ) \, dx \\ & = -\left (2 \int e^{2 x} (1+2 x) \, dx\right )-12 \int e^x (1+x) \, dx+\int \frac {-3 e^{3/x}-17 x+e^{3/x} x+6 x^2}{x} \, dx \\ & = -12 e^x (1+x)-e^{2 x} (1+2 x)+2 \int e^{2 x} \, dx+12 \int e^x \, dx+\int \left (-17+\frac {e^{3/x} (-3+x)}{x}+6 x\right ) \, dx \\ & = 12 e^x+e^{2 x}-17 x+3 x^2-12 e^x (1+x)-e^{2 x} (1+2 x)+\int \frac {e^{3/x} (-3+x)}{x} \, dx \\ & = 12 e^x+e^{2 x}-17 x+e^{3/x} x+3 x^2-12 e^x (1+x)-e^{2 x} (1+2 x) \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.07 \[ \int \frac {e^{3/x} (-3+x)-17 x+6 x^2+e^x \left (-12 x-12 x^2\right )+e^{2 x} \left (-2 x-4 x^2\right )}{x} \, dx=-17 x+e^{3/x} x-12 e^x x-2 e^{2 x} x+3 x^2 \]
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Time = 0.95 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00
method | result | size |
default | \(x \,{\mathrm e}^{\frac {3}{x}}-17 x +3 x^{2}-2 x \,{\mathrm e}^{2 x}-12 \,{\mathrm e}^{x} x\) | \(30\) |
norman | \(x \,{\mathrm e}^{\frac {3}{x}}-17 x +3 x^{2}-2 x \,{\mathrm e}^{2 x}-12 \,{\mathrm e}^{x} x\) | \(30\) |
risch | \(x \,{\mathrm e}^{\frac {3}{x}}-17 x +3 x^{2}-2 x \,{\mathrm e}^{2 x}-12 \,{\mathrm e}^{x} x\) | \(30\) |
parallelrisch | \(x \,{\mathrm e}^{\frac {3}{x}}-17 x +3 x^{2}-2 x \,{\mathrm e}^{2 x}-12 \,{\mathrm e}^{x} x\) | \(30\) |
parts | \(x \,{\mathrm e}^{\frac {3}{x}}-17 x +3 x^{2}-2 x \,{\mathrm e}^{2 x}-12 \,{\mathrm e}^{x} x\) | \(30\) |
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none
Time = 0.25 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.97 \[ \int \frac {e^{3/x} (-3+x)-17 x+6 x^2+e^x \left (-12 x-12 x^2\right )+e^{2 x} \left (-2 x-4 x^2\right )}{x} \, dx=3 \, x^{2} - 2 \, x e^{\left (2 \, x\right )} - 12 \, x e^{x} + x e^{\frac {3}{x}} - 17 \, x \]
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Time = 0.17 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.97 \[ \int \frac {e^{3/x} (-3+x)-17 x+6 x^2+e^x \left (-12 x-12 x^2\right )+e^{2 x} \left (-2 x-4 x^2\right )}{x} \, dx=3 x^{2} + x e^{\frac {3}{x}} - 2 x e^{2 x} - 12 x e^{x} - 17 x \]
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Result contains higher order function than in optimal. Order 4 vs. order 3.
Time = 0.22 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.80 \[ \int \frac {e^{3/x} (-3+x)-17 x+6 x^2+e^x \left (-12 x-12 x^2\right )+e^{2 x} \left (-2 x-4 x^2\right )}{x} \, dx=3 \, x^{2} - {\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} - 12 \, {\left (x - 1\right )} e^{x} - 17 \, x + 3 \, {\rm Ei}\left (\frac {3}{x}\right ) - e^{\left (2 \, x\right )} - 12 \, e^{x} - 3 \, \Gamma \left (-1, -\frac {3}{x}\right ) \]
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Time = 0.26 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.97 \[ \int \frac {e^{3/x} (-3+x)-17 x+6 x^2+e^x \left (-12 x-12 x^2\right )+e^{2 x} \left (-2 x-4 x^2\right )}{x} \, dx=3 \, x^{2} - 2 \, x e^{\left (2 \, x\right )} - 12 \, x e^{x} + x e^{\frac {3}{x}} - 17 \, x \]
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Time = 8.94 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.87 \[ \int \frac {e^{3/x} (-3+x)-17 x+6 x^2+e^x \left (-12 x-12 x^2\right )+e^{2 x} \left (-2 x-4 x^2\right )}{x} \, dx=-x\,\left (2\,{\mathrm {e}}^{2\,x}-3\,x-{\mathrm {e}}^{3/x}+12\,{\mathrm {e}}^x+17\right ) \]
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