Optimal. Leaf size=22 \[ 2-e^{\frac {1}{7-x+x^2}}+2 x+x^6 \]
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Rubi [A] time = 0.30, antiderivative size = 21, normalized size of antiderivative = 0.95, number of steps used = 3, number of rules used = 2, integrand size = 84, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {6688, 6706} \begin {gather*} x^6-e^{\frac {1}{x^2-x+7}}+2 x \end {gather*}
Antiderivative was successfully verified.
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Rule 6688
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (2+6 x^5+\frac {e^{\frac {1}{7-x+x^2}} (-1+2 x)}{\left (7-x+x^2\right )^2}\right ) \, dx\\ &=2 x+x^6+\int \frac {e^{\frac {1}{7-x+x^2}} (-1+2 x)}{\left (7-x+x^2\right )^2} \, dx\\ &=-e^{\frac {1}{7-x+x^2}}+2 x+x^6\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.22, size = 21, normalized size = 0.95 \begin {gather*} -e^{\frac {1}{7-x+x^2}}+2 x+x^6 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.90, size = 20, normalized size = 0.91 \begin {gather*} x^{6} + 2 \, x - e^{\left (\frac {1}{x^{2} - x + 7}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 20, normalized size = 0.91 \begin {gather*} x^{6} + 2 \, x - e^{\left (\frac {1}{x^{2} - x + 7}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.17, size = 21, normalized size = 0.95
method | result | size |
risch | \(x^{6}+2 x -{\mathrm e}^{\frac {1}{x^{2}-x +7}}\) | \(21\) |
norman | \(\frac {x^{8}+12 x +{\mathrm e}^{\frac {1}{x^{2}-x +7}} x +2 x^{3}+7 x^{6}-x^{7}-{\mathrm e}^{\frac {1}{x^{2}-x +7}} x^{2}-7 \,{\mathrm e}^{\frac {1}{x^{2}-x +7}}+14}{x^{2}-x +7}\) | \(77\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.51, size = 188, normalized size = 8.55 \begin {gather*} x^{6} + 2 \, x + \frac {2 \, {\left (12580 \, x - 1673\right )}}{9 \, {\left (x^{2} - x + 7\right )}} - \frac {10 \, {\left (1763 \, x - 2002\right )}}{3 \, {\left (x^{2} - x + 7\right )}} + \frac {28 \, {\left (286 \, x + 1477\right )}}{9 \, {\left (x^{2} - x + 7\right )}} - \frac {4 \, {\left (239 \, x + 12341\right )}}{9 \, {\left (x^{2} - x + 7\right )}} + \frac {98 \, {\left (211 \, x - 497\right )}}{9 \, {\left (x^{2} - x + 7\right )}} + \frac {2 \, {\left (71 \, x + 140\right )}}{27 \, {\left (x^{2} - x + 7\right )}} + \frac {4 \, {\left (20 \, x - 91\right )}}{27 \, {\left (x^{2} - x + 7\right )}} - \frac {10 \, {\left (13 \, x + 7\right )}}{9 \, {\left (x^{2} - x + 7\right )}} + \frac {98 \, {\left (2 \, x - 1\right )}}{27 \, {\left (x^{2} - x + 7\right )}} - \frac {28 \, {\left (x - 14\right )}}{27 \, {\left (x^{2} - x + 7\right )}} - e^{\left (\frac {1}{x^{2} - x + 7}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.24, size = 20, normalized size = 0.91 \begin {gather*} 2\,x-{\mathrm {e}}^{\frac {1}{x^2-x+7}}+x^6 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 15, normalized size = 0.68 \begin {gather*} x^{6} + 2 x - e^{\frac {1}{x^{2} - x + 7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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