Integrand size = 30, antiderivative size = 22 \[ \int \frac {2+e^{e^{\frac {-60+e^4}{e^4}}} x^2+e^x x^2}{x^2} \, dx=e^x-\frac {2}{x}+e^{e^{1-\frac {60}{e^4}}} x \]
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Time = 0.01 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {14, 2225} \[ \int \frac {2+e^{e^{\frac {-60+e^4}{e^4}}} x^2+e^x x^2}{x^2} \, dx=e^{e^{1-\frac {60}{e^4}}} x+e^x-\frac {2}{x} \]
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Rule 14
Rule 2225
Rubi steps \begin{align*} \text {integral}& = \int \left (e^x+\frac {2+e^{e^{1-\frac {60}{e^4}}} x^2}{x^2}\right ) \, dx \\ & = \int e^x \, dx+\int \frac {2+e^{e^{1-\frac {60}{e^4}}} x^2}{x^2} \, dx \\ & = e^x+\int \left (e^{e^{1-\frac {60}{e^4}}}+\frac {2}{x^2}\right ) \, dx \\ & = e^x-\frac {2}{x}+e^{e^{1-\frac {60}{e^4}}} x \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {2+e^{e^{\frac {-60+e^4}{e^4}}} x^2+e^x x^2}{x^2} \, dx=e^x-\frac {2}{x}+e^{e^{1-\frac {60}{e^4}}} x \]
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Time = 0.43 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.86
method | result | size |
risch | \(x \,{\mathrm e}^{{\mathrm e}^{1-60 \,{\mathrm e}^{-4}}}-\frac {2}{x}+{\mathrm e}^{x}\) | \(19\) |
parts | \(x \,{\mathrm e}^{{\mathrm e}^{\left ({\mathrm e}^{4}-60\right ) {\mathrm e}^{-4}}}-\frac {2}{x}+{\mathrm e}^{x}\) | \(20\) |
default | \({\mathrm e}^{x}-\frac {2}{x}+x \,{\mathrm e}^{{\mathrm e} \,{\mathrm e}^{-60 \,{\mathrm e}^{-4}}}\) | \(22\) |
norman | \(\frac {-2+x^{2} {\mathrm e}^{{\mathrm e} \,{\mathrm e}^{-60 \,{\mathrm e}^{-4}}}+{\mathrm e}^{x} x}{x}\) | \(26\) |
parallelrisch | \(\frac {-2+x^{2} {\mathrm e}^{{\mathrm e}^{\left ({\mathrm e}^{4}-60\right ) {\mathrm e}^{-4}}}+{\mathrm e}^{x} x}{x}\) | \(26\) |
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Time = 0.25 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05 \[ \int \frac {2+e^{e^{\frac {-60+e^4}{e^4}}} x^2+e^x x^2}{x^2} \, dx=\frac {x^{2} e^{\left (e^{\left ({\left (e^{4} - 60\right )} e^{\left (-4\right )}\right )}\right )} + x e^{x} - 2}{x} \]
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Time = 0.08 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.86 \[ \int \frac {2+e^{e^{\frac {-60+e^4}{e^4}}} x^2+e^x x^2}{x^2} \, dx=x e^{\frac {e}{e^{\frac {60}{e^{4}}}}} + e^{x} - \frac {2}{x} \]
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Time = 0.20 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.82 \[ \int \frac {2+e^{e^{\frac {-60+e^4}{e^4}}} x^2+e^x x^2}{x^2} \, dx=x e^{\left (e^{\left (-60 \, e^{\left (-4\right )} + 1\right )}\right )} - \frac {2}{x} + e^{x} \]
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Time = 0.25 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05 \[ \int \frac {2+e^{e^{\frac {-60+e^4}{e^4}}} x^2+e^x x^2}{x^2} \, dx=\frac {x^{2} e^{\left (e^{\left ({\left (e^{4} - 60\right )} e^{\left (-4\right )}\right )}\right )} + x e^{x} - 2}{x} \]
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Time = 0.08 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.86 \[ \int \frac {2+e^{e^{\frac {-60+e^4}{e^4}}} x^2+e^x x^2}{x^2} \, dx={\mathrm {e}}^x+x\,{\mathrm {e}}^{{\mathrm {e}}^{-60\,{\mathrm {e}}^{-4}}\,\mathrm {e}}-\frac {2}{x} \]
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