Integrand size = 42, antiderivative size = 23 \[ \int \frac {e^{\frac {4+x^2-2 x^3-6 x^5}{x}} \left (-20+5 x^2-20 x^3-120 x^5\right )}{x^2} \, dx=5 e^{\frac {4}{x}+x-2 x^3 \left (\frac {1}{x}+3 x\right )} \]
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Time = 0.22 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {6838} \[ \int \frac {e^{\frac {4+x^2-2 x^3-6 x^5}{x}} \left (-20+5 x^2-20 x^3-120 x^5\right )}{x^2} \, dx=5 e^{\frac {-6 x^5-2 x^3+x^2+4}{x}} \]
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Rule 6838
Rubi steps \begin{align*} \text {integral}& = 5 e^{\frac {4+x^2-2 x^3-6 x^5}{x}} \\ \end{align*}
Time = 0.07 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.91 \[ \int \frac {e^{\frac {4+x^2-2 x^3-6 x^5}{x}} \left (-20+5 x^2-20 x^3-120 x^5\right )}{x^2} \, dx=5 e^{\frac {4}{x}+x-2 x^2-6 x^4} \]
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Time = 0.09 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00
method | result | size |
norman | \(5 \,{\mathrm e}^{\frac {-6 x^{5}-2 x^{3}+x^{2}+4}{x}}\) | \(23\) |
gosper | \(5 \,{\mathrm e}^{-\frac {6 x^{5}+2 x^{3}-x^{2}-4}{x}}\) | \(26\) |
risch | \(5 \,{\mathrm e}^{-\frac {6 x^{5}+2 x^{3}-x^{2}-4}{x}}\) | \(26\) |
parallelrisch | \(5 \,{\mathrm e}^{-\frac {6 x^{5}+2 x^{3}-x^{2}-4}{x}}\) | \(26\) |
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Time = 0.23 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.09 \[ \int \frac {e^{\frac {4+x^2-2 x^3-6 x^5}{x}} \left (-20+5 x^2-20 x^3-120 x^5\right )}{x^2} \, dx=5 \, e^{\left (-\frac {6 \, x^{5} + 2 \, x^{3} - x^{2} - 4}{x}\right )} \]
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Time = 0.07 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int \frac {e^{\frac {4+x^2-2 x^3-6 x^5}{x}} \left (-20+5 x^2-20 x^3-120 x^5\right )}{x^2} \, dx=5 e^{\frac {- 6 x^{5} - 2 x^{3} + x^{2} + 4}{x}} \]
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none
Time = 0.25 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87 \[ \int \frac {e^{\frac {4+x^2-2 x^3-6 x^5}{x}} \left (-20+5 x^2-20 x^3-120 x^5\right )}{x^2} \, dx=5 \, e^{\left (-6 \, x^{4} - 2 \, x^{2} + x + \frac {4}{x}\right )} \]
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Time = 0.25 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87 \[ \int \frac {e^{\frac {4+x^2-2 x^3-6 x^5}{x}} \left (-20+5 x^2-20 x^3-120 x^5\right )}{x^2} \, dx=5 \, e^{\left (-6 \, x^{4} - 2 \, x^{2} + x + \frac {4}{x}\right )} \]
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Time = 7.96 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.96 \[ \int \frac {e^{\frac {4+x^2-2 x^3-6 x^5}{x}} \left (-20+5 x^2-20 x^3-120 x^5\right )}{x^2} \, dx=5\,{\mathrm {e}}^{-2\,x^2}\,{\mathrm {e}}^{4/x}\,{\mathrm {e}}^{-6\,x^4}\,{\mathrm {e}}^x \]
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