Optimal. Leaf size=22 \[ 1+e^{-1+(-1+x) x}+\left (e^5-\frac {4}{x^2}\right )^2 \]
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Rubi [A] time = 0.05, antiderivative size = 24, normalized size of antiderivative = 1.09, number of steps used = 5, number of rules used = 2, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {14, 2236} \begin {gather*} \frac {16}{x^4}+e^{x^2-x-1}-\frac {8 e^5}{x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2236
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (e^{-1-x+x^2} (-1+2 x)+\frac {16 \left (-4+e^5 x^2\right )}{x^5}\right ) \, dx\\ &=16 \int \frac {-4+e^5 x^2}{x^5} \, dx+\int e^{-1-x+x^2} (-1+2 x) \, dx\\ &=e^{-1-x+x^2}+16 \int \left (-\frac {4}{x^5}+\frac {e^5}{x^3}\right ) \, dx\\ &=e^{-1-x+x^2}+\frac {16}{x^4}-\frac {8 e^5}{x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.05, size = 24, normalized size = 1.09 \begin {gather*} e^{-1-x+x^2}+\frac {16}{x^4}-\frac {8 e^5}{x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 26, normalized size = 1.18 \begin {gather*} \frac {x^{4} e^{\left (x^{2} - x - 1\right )} - 8 \, x^{2} e^{5} + 16}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 30, normalized size = 1.36 \begin {gather*} \frac {{\left (x^{4} e^{\left (x^{2} - x\right )} - 8 \, x^{2} e^{6} + 16 \, e\right )} e^{\left (-1\right )}}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 23, normalized size = 1.05
method | result | size |
default | \(\frac {16}{x^{4}}-\frac {8 \,{\mathrm e}^{5}}{x^{2}}+{\mathrm e}^{x^{2}-x -1}\) | \(23\) |
risch | \(\frac {-8 x^{2} {\mathrm e}^{5}+16}{x^{4}}+{\mathrm e}^{x^{2}-x -1}\) | \(24\) |
norman | \(\frac {16+x^{4} {\mathrm e}^{x^{2}-x -1}-8 x^{2} {\mathrm e}^{5}}{x^{4}}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.40, size = 79, normalized size = 3.59 \begin {gather*} \frac {1}{2} i \, \sqrt {\pi } \operatorname {erf}\left (i \, x - \frac {1}{2} i\right ) e^{\left (-\frac {5}{4}\right )} + \frac {1}{2} \, {\left (\frac {\sqrt {\pi } {\left (2 \, x - 1\right )} {\left (\operatorname {erf}\left (\frac {1}{2} \, \sqrt {-{\left (2 \, x - 1\right )}^{2}}\right ) - 1\right )}}{\sqrt {-{\left (2 \, x - 1\right )}^{2}}} + 2 \, e^{\left (\frac {1}{4} \, {\left (2 \, x - 1\right )}^{2}\right )}\right )} e^{\left (-\frac {5}{4}\right )} - \frac {8 \, e^{5}}{x^{2}} + \frac {16}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 8.38, size = 24, normalized size = 1.09 \begin {gather*} {\mathrm {e}}^{x^2-x-1}-\frac {8\,x^2\,{\mathrm {e}}^5-16}{x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 20, normalized size = 0.91 \begin {gather*} e^{x^{2} - x - 1} + \frac {- 8 x^{2} e^{5} + 16}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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