Integrand size = 39, antiderivative size = 30 \[ \int \frac {90-60 x+15 x^2+e^{e^x+x} \left (60-60 x+15 x^2\right )}{4-4 x+x^2} \, dx=15 \left (-1-e^{e^{e^{e^5}}}+e^{e^x}+x+\frac {x}{2-x}\right ) \]
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Time = 0.08 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.67, number of steps used = 7, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.128, Rules used = {27, 6874, 2320, 2225, 697} \[ \int \frac {90-60 x+15 x^2+e^{e^x+x} \left (60-60 x+15 x^2\right )}{4-4 x+x^2} \, dx=15 x+15 e^{e^x}+\frac {30}{2-x} \]
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Rule 27
Rule 697
Rule 2225
Rule 2320
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int \frac {90-60 x+15 x^2+e^{e^x+x} \left (60-60 x+15 x^2\right )}{(-2+x)^2} \, dx \\ & = \int \left (15 e^{e^x+x}+\frac {15 \left (6-4 x+x^2\right )}{(-2+x)^2}\right ) \, dx \\ & = 15 \int e^{e^x+x} \, dx+15 \int \frac {6-4 x+x^2}{(-2+x)^2} \, dx \\ & = 15 \int \left (1+\frac {2}{(-2+x)^2}\right ) \, dx+15 \text {Subst}\left (\int e^x \, dx,x,e^x\right ) \\ & = 15 e^{e^x}+\frac {30}{2-x}+15 x \\ \end{align*}
Time = 0.06 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.60 \[ \int \frac {90-60 x+15 x^2+e^{e^x+x} \left (60-60 x+15 x^2\right )}{4-4 x+x^2} \, dx=15 \left (e^{e^x}+\frac {2}{2-x}+x\right ) \]
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Time = 0.52 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.57
method | result | size |
risch | \(-\frac {30}{-2+x}+15 x +15 \,{\mathrm e}^{{\mathrm e}^{x}}\) | \(17\) |
parts | \(-\frac {30}{-2+x}+15 x +15 \,{\mathrm e}^{{\mathrm e}^{x}}\) | \(17\) |
norman | \(\frac {15 x^{2}+15 x \,{\mathrm e}^{{\mathrm e}^{x}}-30 \,{\mathrm e}^{{\mathrm e}^{x}}-90}{-2+x}\) | \(25\) |
parallelrisch | \(\frac {15 x^{2}+15 x \,{\mathrm e}^{{\mathrm e}^{x}}-30 \,{\mathrm e}^{{\mathrm e}^{x}}-90}{-2+x}\) | \(25\) |
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Time = 0.26 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.07 \[ \int \frac {90-60 x+15 x^2+e^{e^x+x} \left (60-60 x+15 x^2\right )}{4-4 x+x^2} \, dx=\frac {15 \, {\left ({\left (x - 2\right )} e^{\left (x + e^{x}\right )} + {\left (x^{2} - 2 \, x - 2\right )} e^{x}\right )} e^{\left (-x\right )}}{x - 2} \]
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Time = 0.10 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.47 \[ \int \frac {90-60 x+15 x^2+e^{e^x+x} \left (60-60 x+15 x^2\right )}{4-4 x+x^2} \, dx=15 x + 15 e^{e^{x}} - \frac {30}{x - 2} \]
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Time = 0.26 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.53 \[ \int \frac {90-60 x+15 x^2+e^{e^x+x} \left (60-60 x+15 x^2\right )}{4-4 x+x^2} \, dx=15 \, x - \frac {30}{x - 2} + 15 \, e^{\left (e^{x}\right )} \]
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Time = 0.27 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.43 \[ \int \frac {90-60 x+15 x^2+e^{e^x+x} \left (60-60 x+15 x^2\right )}{4-4 x+x^2} \, dx=\frac {15 \, {\left (x^{2} e^{x} + x e^{\left (x + e^{x}\right )} - 2 \, x e^{x} - 2 \, e^{\left (x + e^{x}\right )} - 2 \, e^{x}\right )}}{x e^{x} - 2 \, e^{x}} \]
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Time = 14.61 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.53 \[ \int \frac {90-60 x+15 x^2+e^{e^x+x} \left (60-60 x+15 x^2\right )}{4-4 x+x^2} \, dx=15\,x+15\,{\mathrm {e}}^{{\mathrm {e}}^x}-\frac {30}{x-2} \]
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