Optimal. Leaf size=21 \[ 3-e^{\left (-\frac {1}{x^4}+x\right )^2}-x+x^6 \]
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Rubi [A] time = 0.40, antiderivative size = 24, normalized size of antiderivative = 1.14, number of steps used = 3, number of rules used = 2, integrand size = 44, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {14, 6706} \begin {gather*} x^6-e^{\frac {\left (1-x^5\right )^2}{x^8}}-x \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1+6 x^5-\frac {2 e^{\frac {\left (-1+x^5\right )^2}{x^8}} (-1+x) \left (1+x+x^2+x^3+x^4\right ) \left (4+x^5\right )}{x^9}\right ) \, dx\\ &=-x+x^6-2 \int \frac {e^{\frac {\left (-1+x^5\right )^2}{x^8}} (-1+x) \left (1+x+x^2+x^3+x^4\right ) \left (4+x^5\right )}{x^9} \, dx\\ &=-e^{\frac {\left (1-x^5\right )^2}{x^8}}-x+x^6\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.09, size = 23, normalized size = 1.10 \begin {gather*} -e^{\frac {1}{x^8}-\frac {2}{x^3}+x^2}-x+x^6 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 24, normalized size = 1.14 \begin {gather*} x^{6} - x - e^{\left (\frac {x^{10} - 2 \, x^{5} + 1}{x^{8}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 24, normalized size = 1.14 \begin {gather*} x^{6} - x - e^{\left (\frac {x^{10} - 2 \, x^{5} + 1}{x^{8}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 34, normalized size = 1.62
method | result | size |
norman | \(\frac {x^{14}-x^{9}-{\mathrm e}^{\frac {x^{10}-2 x^{5}+1}{x^{8}}} x^{8}}{x^{8}}\) | \(34\) |
risch | \(x^{6}-x -{\mathrm e}^{\frac {\left (x -1\right )^{2} \left (x^{4}+x^{3}+x^{2}+x +1\right )^{2}}{x^{8}}}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 22, normalized size = 1.05 \begin {gather*} x^{6} - x - e^{\left (x^{2} - \frac {2}{x^{3}} + \frac {1}{x^{8}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.85, size = 23, normalized size = 1.10 \begin {gather*} x^6-x-{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{\frac {1}{x^8}}\,{\mathrm {e}}^{-\frac {2}{x^3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 19, normalized size = 0.90 \begin {gather*} x^{6} - x - e^{\frac {x^{10} - 2 x^{5} + 1}{x^{8}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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